japanese translation updated for differential equations. 90/14490/2
Rui Hirokawa [Fri, 2 May 2014 12:26:36 +0000 (21:26 +0900)]
Change-Id: Ie16c6e019781bc0accb8879fff345a7380dc16c4

27 files changed:
scilab/modules/differential_equations/help/ja_JP/bvode.xml
scilab/modules/differential_equations/help/ja_JP/dae.xml
scilab/modules/differential_equations/help/ja_JP/daeoptions.xml
scilab/modules/differential_equations/help/ja_JP/daskr.xml
scilab/modules/differential_equations/help/ja_JP/dasrt.xml
scilab/modules/differential_equations/help/ja_JP/dassl.xml
scilab/modules/differential_equations/help/ja_JP/diff.xml
scilab/modules/differential_equations/help/ja_JP/feval.xml
scilab/modules/differential_equations/help/ja_JP/impl.xml
scilab/modules/differential_equations/help/ja_JP/int2d.xml
scilab/modules/differential_equations/help/ja_JP/int3d.xml
scilab/modules/differential_equations/help/ja_JP/intc.xml
scilab/modules/differential_equations/help/ja_JP/integrate.xml
scilab/modules/differential_equations/help/ja_JP/intg.xml
scilab/modules/differential_equations/help/ja_JP/intl.xml
scilab/modules/differential_equations/help/ja_JP/intsplin.xml
scilab/modules/differential_equations/help/ja_JP/inttrap.xml
scilab/modules/differential_equations/help/ja_JP/numdiff.xml
scilab/modules/differential_equations/help/ja_JP/ode.xml
scilab/modules/differential_equations/help/ja_JP/ode_discrete.xml
scilab/modules/differential_equations/help/ja_JP/ode_root.xml
scilab/modules/differential_equations/help/ja_JP/odedc.xml
scilab/modules/differential_equations/help/ja_JP/odeoptions.xml
scilab/modules/helptools/images/bvode_ja_JP_1.png [new file with mode: 0644]
scilab/modules/helptools/images/bvode_ja_JP_2.png [new file with mode: 0644]
scilab/modules/helptools/images/intg_ja_JP_1.png [new file with mode: 0644]
scilab/modules/helptools/images/intg_ja_JP_2.png [new file with mode: 0644]

index 6574cf9..a1cb992 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt
  *
  -->
+
 <refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="bvode" xml:lang="ja">
+    
     <refnamediv>
+        
         <refname>bvode</refname>
+        
         <refpurpose>コロケーション法によるODEの境界値問題</refpurpose>
+        
     </refnamediv>
+    
     <refnamediv xml:id="bvodeS">
+        
         <refname>bvodeS</refname>
+        
         <refpurpose>bvodeの簡易的なコール</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>
+            
             zu=bvode(xpoints,N,m,x_low,x_up,zeta,ipar,ltol,tol,fixpnt,fsub,dfsub,gsub,dgsub,guess)
+            
         </synopsis>
+        
         <synopsis>
+            
             zu=bvodeS(xpoints,m,N,x_low,x_up,fsub,gsub,zeta, &lt;optional_args&gt;)
+            
         </synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>zu</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         大きさMの列ベクトル.
+                        
                         複数の点で指定したメッシュ上で評価したODEの解.
+                        
                         各点における z(u(x)) が含まれます.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>xpoints</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         解を観測する点を指定する配列.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>N</term>
+                
                 <listitem>
+                    
                     <para>整数値を有するスカラー,微分方程式の数
+                        
                         (N &lt;= 20).
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>m</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         整数要素を有する大きさ <literal>N</literal> のベクトル.
+                        
                         <literal>m</literal>は各微分方程式の次数のベクトルで,
+                        
                         <literal>m(i)</literal>はi番目の微分方程式の次数を指定します.
+                        
                         以下に示す <literal>M</literal>は
+                        
                         <literal>m</literal>の要素の合計を表します.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>x_low</term>
+                
                 <listitem>
+                    
                     <para>スカラー: 区間の左端</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>x_up</term>
+                
                 <listitem>
+                    
                     <para>スカラー: 区間の右端</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>zeta</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         大きさ Mのベクトル,<literal>zeta(j)</literal> 
+                        
                         は, j番目の端の条件点(境界値)を指定します.
+                        
                         x_low&lt;=zeta(j)
+                        
                         &lt;= zeta(j+1)<literal>&lt;=x_up</literal>
+                        
                         となります.
+                        
                     </para>
+                    
                     <para>
+                        
                         全ての境界条件点は,
+                        
                         使用される全てのメッシュにおけるメッシュ点とする必要があります.
+                        
                         以下の <literal>ipar(11)</literal> および
+                        
                         <literal>fixpnt</literal>の説明を参照ください.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>ipar</term>
+                
                 <listitem>
+                    
                     <para>11個の整数要素を有する配列:</para>
+                    
                     <para>
+                        
                         [<literal>nonlin, collpnt, subint, ntol, ndimf, ndimi, iprint,
+                            
                             iread, iguess, rstart,nfxpnt]
+                            
                         </literal>
+                        
                     </para>
+                    
                     <variablelist>
+                        
                         <varlistentry>
+                            
                             <term>nonlin: ipar(1)</term>
+                            
                             <listitem>
+                                
                                 <para>問題が線形の場合: 0 ,問題が非線形の場合: 1</para>
+                                
                             </listitem>
+                            
                         </varlistentry>
+                        
                         <varlistentry>
+                            
                             <term>collpnt: ipar(2)</term>
+                            
                             <listitem>
+                                
                                 <para>
+                                    
                                     サブ区間毎のコロケーション点の数を指定します.
+                                    
                                     ただし, 
+                                    
                                     where max(m(j)) &lt;= collpnt &lt;= 7
+                                    
                                 </para>
+                                
                                 <para>
+                                    
                                     <literal>ipar(2)=0</literal> の場合,
+                                    
                                     <literal>collpnt</literal> は ( max(m(j))+1 ,
+                                    
                                     5-max(m(j)) )に設定されます
+                                    
                                 </para>
+                                
                             </listitem>
+                            
                         </varlistentry>
+                        
                         <varlistentry>
+                            
                             <term>subint: ipar(3)</term>
+                            
                             <listitem>
+                                
                                 <para>初期メッシュのサブ区間の数を指定します.
+                                    
                                     <literal>ipar(3) = 0</literal> の場合,
+                                    
                                     適宜 
+                                    
                                     <literal>subint = 5</literal>と設定します.
+                                    
                                 </para>
+                                
                             </listitem>
+                            
                         </varlistentry>
+                        
                         <varlistentry>
+                            
                             <term>ntol: ipar(4)</term>
+                            
                             <listitem>
+                                
                                 <para>
+                                    
                                     解と微分の許容誤差の数を指定します.
+                                    
                                     0 &lt; ntol &lt;= M とする必要があります.
+                                    
                                     <literal>ipar(4)</literal> は,
+                                    
                                     <literal>tol</literal> 引数の次元または
+                                    
                                     <literal>0</literal>に設定する必要があります.
+                                    
                                     後者の場合, 実際の値は自動的に
+                                    
                                     <literal>size(tol,'*')</literal> に設定されます.
+                                    
                                 </para>
+                                
                             </listitem>
+                            
                         </varlistentry>
+                        
                         <varlistentry>
+                            
                             <term>ndimf: ipar(5)</term>
+                            
                             <listitem>
+                                
                                 <para>
+                                    
                                     <literal>fspace</literal>(実数の作業配列)の次元を指定します.
+                                    
                                     この値は, 
+                                    
                                     サブ区間の最大数 nmax への拘束条件を指定します.
+                                    
                                 </para>
+                                
                                 <para>ipar(5) の値は,拘束条件
+                                    
                                     ipar(5)&gt;=nmax*nsizef を考慮する必要があります. ただし
+                                    
                                 </para>
+                                
                                 <para>
+                                    
                                     <literal>nsizef=4+3*M+(5+collpnt*N)*(collpnt*N+M)+(2*M-nrec)*2*M</literal>
+                                    
                                     (<literal>nrec</literal> は終端境界条件の数です
+                                    
                                     ).
+                                    
                                 </para>
+                                
                             </listitem>
+                            
                         </varlistentry>
+                        
                         <varlistentry>
+                            
                             <term>ndimi: ipar(6)</term>
+                            
                             <listitem>
+                                
                                 <para>ispace (整数作業配列)の次元を指定します.
+                                    
                                     この値は, サブ区間の最大数 nmax への拘束条件を指定します.
+                                    
                                 </para>
+                                
                                 <para>ipar(6) の値は, 拘束条件 ipar(6)&gt;=nmax*nsizei
+                                    
                                     を考慮する必要があります. ただし,
+                                    
                                 </para>
+                                
                                 <para>
+                                    
                                     <literal>nsizei=3 +
+                                        
                                     </literal>
+                                    
                                     <literal>collpnt*N+M</literal>.
+                                    
                                 </para>
+                                
                             </listitem>
+                            
                         </varlistentry>
+                        
                         <varlistentry>
+                            
                             <term>iprint: ipar(7)</term>
+                            
                             <listitem>
+                                
                                 <para>出力制御, 以下の値とします:</para>
+                                
                                 <variablelist>
+                                    
                                     <varlistentry>
+                                        
                                         <term>-1</term>
+                                        
                                         <listitem>
+                                            
                                             <para>完全な診断出力の場合</para>
+                                            
                                         </listitem>
+                                        
                                     </varlistentry>
+                                    
                                     <varlistentry>
+                                        
                                         <term>0</term>
+                                        
                                         <listitem>
+                                            
                                             <para>部分的な出力の場合</para>
+                                            
                                         </listitem>
+                                        
                                     </varlistentry>
+                                    
                                     <varlistentry>
+                                        
                                         <term>1</term>
+                                        
                                         <listitem>
+                                            
                                             <para>出力しない場合</para>
+                                            
                                         </listitem>
+                                        
                                     </varlistentry>
+                                    
                                 </variablelist>
+                                
                             </listitem>
+                            
                         </varlistentry>
+                        
                         <varlistentry>
+                            
                             <term>iread: ipar(8)</term>
+                            
                             <listitem>
+                                
                                 <variablelist>
+                                    
                                     <varlistentry>
+                                        
                                         <term>= 0</term>
+                                        
                                         <listitem>
+                                            
                                             <para>
+                                                
                                                 bvodeが一様な初期メッシュを生成するようにします.
+                                                
                                             </para>
+                                            
                                         </listitem>
+                                        
                                     </varlistentry>
+                                    
                                     <varlistentry>
+                                        
                                         <term>= xx</term>
+                                        
                                         <listitem>
+                                            
                                             <para>他の値は, Scilabでは未実装です.</para>
+                                            
                                             <variablelist>
+                                                
                                                 <varlistentry>
+                                                    
                                                     <term>= 1</term>
+                                                    
                                                     <listitem>
+                                                        
                                                         <para>初期メッシュがユーザにより指定される場合.
+                                                            
                                                             fspace で以下のように定義されます: 
+                                                            
                                                         </para>
+                                                        
                                                         <para>
+                                                            
                                                             メッシュは <literal>fspace(1), ...,
+                                                                
                                                                 fspace(n+1)
+                                                                
                                                             </literal>
+                                                            
                                                             となります. 
+                                                            
                                                             ユーザは内部メッシュ点<literal>fspace(j) = x(j),
+                                                                
                                                                 j = 2, ..., n.
+                                                                
                                                             </literal>
+                                                            
                                                             のみを指定する必要があります.
+                                                            
                                                         </para>
+                                                        
                                                     </listitem>
+                                                    
                                                 </varlistentry>
+                                                
                                                 <varlistentry>
+                                                    
                                                     <term>= 2 初期メッシュがユーザにより指定される場合.</term>
+                                                    
                                                     <listitem>
+                                                        
                                                         <para>
+                                                            
                                                             <literal>ipar(8)=1</literal>が指定された時と同様であり, 
+                                                            
                                                             加えて,適応型メッシュ選択は行われません.
+                                                            
                                                         </para>
+                                                        
                                                     </listitem>
+                                                    
                                                 </varlistentry>
+                                                
                                             </variablelist>
+                                            
                                         </listitem>
+                                        
                                     </varlistentry>
+                                    
                                 </variablelist>
+                                
                             </listitem>
+                            
                         </varlistentry>
+                        
                         <varlistentry>
+                            
                             <term>iguess: ipar(9)</term>
+                            
                             <listitem>
+                                
                                 <variablelist>
+                                    
                                     <varlistentry>
+                                        
                                         <term>= 0</term>
+                                        
                                         <listitem>
+                                            
                                             <para>解の初期推定値が指定されない場合.</para>
+                                            
                                         </listitem>
+                                        
                                     </varlistentry>
+                                    
                                     <varlistentry>
+                                        
                                         <term>= 1</term>
+                                        
                                         <listitem>
+                                            
                                             <para>
+                                                
                                                 引数 <literal>guess</literal> により,
+                                                
                                                 初期推定値がユーザにより指定される場合.
+                                                
                                             </para>
+                                            
                                         </listitem>
+                                        
                                     </varlistentry>
+                                    
                                     <varlistentry>
+                                        
                                         <term>= 2</term>
+                                        
                                         <listitem>
+                                            
                                             <para>
+                                                
                                                 初期メッシュと近似解係数がユーザにより fspace で指定される場合
+                                                
                                                 (前のメッシュと新規メッシュは同じものになります).
+                                                
                                             </para>
+                                            
                                         </listitem>
+                                        
                                     </varlistentry>
+                                    
                                     <varlistentry>
+                                        
                                         <term>= 3</term>
+                                        
                                         <listitem>
+                                            
                                             <para>
+                                                
                                                 前のメッシュと近似解の係数がユーザによりfspace で指定される場合,
+                                                
                                                 新規メッシュは 2倍荒くとられます.
+                                                
                                                 すなわち, 前のメッシュの各2点毎に1点となります.
+                                                
                                             </para>
+                                            
                                         </listitem>
+                                        
                                     </varlistentry>
+                                    
                                     <varlistentry>
+                                        
                                         <term>= 4</term>
+                                        
                                         <listitem>
+                                            
                                             <para>
+                                                
                                                 前の初期メッシュと近似解係数に加えて,同時に
+                                                
                                                 新規メッシュが fspace に出力されます.
+                                                
                                                 (詳細はiguess = 2, 3, および 4の出力の説明を参照ください)
+                                                
                                             </para>
+                                            
                                         </listitem>
+                                        
                                     </varlistentry>
+                                    
                                 </variablelist>
+                                
                             </listitem>
+                            
                         </varlistentry>
+                        
                         <varlistentry>
+                            
                             <term>ireg: ipar(10)</term>
+                            
                             <listitem>
+                                
                                 <variablelist>
+                                    
                                     <varlistentry>
+                                        
                                         <term>= 0</term>
+                                        
                                         <listitem>
+                                            
                                             <para>問題が標準の場合</para>
+                                            
                                         </listitem>
+                                        
                                     </varlistentry>
+                                    
                                     <varlistentry>
+                                        
                                         <term>= 1</term>
+                                        
                                         <listitem>
+                                            
                                             <para>
+                                                
                                                 最初の緩和係数が <literal>ireg</literal> に等しい場合,
+                                                
                                                 非線形反復は過去の収束結果に基づきません.
+                                                
                                                 (別の敏感な非線形問題のみで使用されます)
+                                                
                                             </para>
+                                            
                                         </listitem>
+                                        
                                     </varlistentry>
+                                    
                                     <varlistentry>
+                                        
                                         <term>= 2</term>
+                                        
                                         <listitem>
+                                            
                                             <para>
+                                                
                                                 以下の場合,直ちにリターンします.
+                                                
                                                 (a) 2回連続で収束しない場合,
+                                                
                                                 または
+                                                
                                                 (b)最初に誤差推定値を得た後.
+                                                
                                             </para>
+                                            
                                         </listitem>
+                                        
                                     </varlistentry>
+                                    
                                 </variablelist>
+                                
                             </listitem>
+                            
                         </varlistentry>
+                        
                         <varlistentry>
+                            
                             <term>nfxpnt: ipar(11)</term>
+                            
                             <listitem>
+                                
                                 <para>
+                                    
                                     <literal>x_low</literal> および <literal>x_up</literal>
+                                    
                                     以外のメッシュの固定点の数(<literal>fixpnt</literal>の次元)を指定します.
+                                    
                                     <literal>ipar(11)</literal> は,引数
+                                    
                                     <literal>fixpnt</literal>の次元または
+                                    
                                     <literal>0</literal>に設定する必要があります.
+                                    
                                     後者の場合, 実際の値は自動的に
+                                    
                                     <literal>size(fixpnt,'*')</literal> に設定されます.
+                                    
                                 </para>
+                                
                             </listitem>
+                            
                         </varlistentry>
+                        
                     </variablelist>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>ltol</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         次元 <literal>ntol=ipar(4)</literal>の配列.
+                        
                         <literal>ltol(j) = l</literal> は,
+                        
                         <literal> tol</literal> 配列の <literal>j</literal>番目の許容誤差を指定します.これは,
+                        
                         以下の<literal>l</literal>番目の要素の誤差を制御します.
+                        
                         <inlinemediaobject>
+                            
                             <imageobject>
+                                
                                 <imagedata>
+                                    
                                     <mml:math>
+                                        
                                         <mml:semantics>
+                                            
                                             <mml:mi>z</mml:mi>
+                                            
                                             <mml:mrow>
+                                                
                                                 <mml:mo mml:stretchy="false">(</mml:mo><mml:mi>u</mml:mi><mml:mo mml:stretchy="false">)</mml:mo>
+                                                
                                             </mml:mrow>
+                                            
                                         </mml:semantics>
+                                        
                                     </mml:math>
+                                    
                                 </imagedata>
+                                
                             </imageobject>
+                            
                         </inlinemediaobject>
+                        
                         .以下も必要です:
+                        
                     </para>
+                    
                     <para>
+                        
                         <literal>1 &lt;= ltol(1) &lt; ltol(2) &lt; ... &lt; ltol(ntol)
+                            
                             &lt;= M
+                            
                         </literal>
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>tol</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         <literal>ntol=ipar(4)</literal>次の配列.
+                        
                     </para>
+                    
                     <para>
+                        
                         <literal>tol(j)</literal>は,
+                        
                         以下の <literal>ltol(j)</literal> 番目の要素の許容誤差です.
+                        
                         <inlinemediaobject>
+                            
                             <imageobject>
+                                
                                 <imagedata>
+                                    
                                     <mml:math>
+                                        
                                         <mml:semantics>
+                                            
                                             <mml:mi>z</mml:mi>
+                                            
                                             <mml:mrow>
+                                                
                                                 <mml:mo mml:stretchy="false">(</mml:mo><mml:mi>u</mml:mi><mml:mo mml:stretchy="false">)</mml:mo>
+                                                
                                             </mml:mrow>
+                                            
                                         </mml:semantics>
+                                        
                                     </mml:math>
+                                    
                                 </imagedata>
+                                
                             </imageobject>
+                            
                         </inlinemediaobject>
+                        
                         .つまり, このコードは以下の条件を
+                        
                         満たそうとします.
+                        
                         <inlinemediaobject>
+                            
                             <imageobject>
+                                
                                 <imagedata>
+                                    
                                     <mml:math>
+                                        
                                         <mml:semantics>
+                                            
                                             <mml:mrow>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mfenced mml:close="∣" mml:open="∣">
+                                                        
                                                         <mml:msub>
+                                                            
                                                             <mml:mrow>
+                                                                
                                                                 <mml:mo mml:stretchy="false">(</mml:mo>
+                                                                
                                                                 <mml:mrow>
+                                                                    
                                                                     <mml:mi>z</mml:mi>
+                                                                    
                                                                     <mml:mrow>
+                                                                        
                                                                         <mml:mrow>
+                                                                            
                                                                             <mml:mo mml:stretchy="false">(</mml:mo><mml:mi>v</mml:mi><mml:mo mml:stretchy="false">)</mml:mo>
+                                                                            
                                                                         </mml:mrow>
+                                                                        
                                                                         <mml:mo mml:stretchy="false">−</mml:mo><mml:mi>z</mml:mi>
+                                                                        
                                                                     </mml:mrow>
+                                                                    
                                                                     <mml:mrow>
+                                                                        
                                                                         <mml:mo mml:stretchy="false">(</mml:mo><mml:mi>u</mml:mi><mml:mo mml:stretchy="false">)</mml:mo>
+                                                                        
                                                                     </mml:mrow>
+                                                                    
                                                                 </mml:mrow>
+                                                                
                                                                 <mml:mo mml:stretchy="false">)</mml:mo>
+                                                                
                                                             </mml:mrow>
+                                                            
                                                             <mml:mrow>
+                                                                
                                                                 <mml:mi mml:fontstyle="italic">ltol</mml:mi>
+                                                                
                                                                 <mml:mrow>
+                                                                    
                                                                     <mml:mo mml:stretchy="false">(</mml:mo><mml:mi>j</mml:mi><mml:mo mml:stretchy="false">)</mml:mo>
+                                                                    
                                                                 </mml:mrow>
+                                                                
                                                             </mml:mrow>
+                                                            
                                                         </mml:msub>
+                                                        
                                                     </mml:mfenced>
+                                                    
                                                     <mml:mo mml:stretchy="false">≤</mml:mo><mml:mi mml:fontstyle="italic">tol</mml:mi>
+                                                    
                                                 </mml:mrow>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">(</mml:mo><mml:mi>j</mml:mi><mml:mo mml:stretchy="false">)</mml:mo>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                         <mml:mo mml:stretchy="false">⋅</mml:mo>
+                                                        
                                                         <mml:mfenced mml:close="∣" mml:open="∣">
+                                                            
                                                             <mml:msub>
+                                                                
                                                                 <mml:mrow>
+                                                                    
                                                                     <mml:mo mml:stretchy="false">(</mml:mo>
+                                                                    
                                                                     <mml:mrow>
+                                                                        
                                                                         <mml:mi>z</mml:mi>
+                                                                        
                                                                         <mml:mrow>
+                                                                            
                                                                             <mml:mo mml:stretchy="false">(</mml:mo><mml:mi>u</mml:mi><mml:mo mml:stretchy="false">)</mml:mo>
+                                                                            
                                                                         </mml:mrow>
+                                                                        
                                                                     </mml:mrow>
+                                                                    
                                                                     <mml:mo mml:stretchy="false">)</mml:mo>
+                                                                    
                                                                 </mml:mrow>
+                                                                
                                                                 <mml:mrow>
+                                                                    
                                                                     <mml:mi mml:fontstyle="italic">ltol</mml:mi>
+                                                                    
                                                                     <mml:mrow>
+                                                                        
                                                                         <mml:mo mml:stretchy="false">(</mml:mo><mml:mi>j</mml:mi><mml:mo mml:stretchy="false">)</mml:mo>
+                                                                        
                                                                     </mml:mrow>
+                                                                    
                                                                 </mml:mrow>
+                                                                
                                                             </mml:msub>
+                                                            
                                                         </mml:mfenced>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                     <mml:mo mml:stretchy="false">+</mml:mo><mml:mi mml:fontstyle="italic">tol</mml:mi>
+                                                    
                                                 </mml:mrow>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mo mml:stretchy="false">(</mml:mo><mml:mi>j</mml:mi><mml:mo mml:stretchy="false">)</mml:mo>
+                                                    
                                                 </mml:mrow>
+                                                
                                                 <mml:mi>,</mml:mi><mml:mi mml:fontstyle="normal">for</mml:mi>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mi>j</mml:mi><mml:mo mml:stretchy="false">=</mml:mo><mml:mn>1</mml:mn>
+                                                    
                                                 </mml:mrow>
+                                                
                                                 <mml:mi mml:fontstyle="normal">:</mml:mi><mml:mi mml:fontstyle="normal">ntol</mml:mi>
+                                                
                                             </mml:mrow>
+                                            
                                             <mml:annotation mml:encoding="StarMath 5.0">abs(z(v)-z(u))_{ltol(j)}
+                                                
                                                 &lt;= tol(j) cdot abs(z(u))_{ltol(j)} + tol(j), for
+                                                
                                                 j=1:ntol
+                                                
                                             </mml:annotation>
+                                            
                                         </mml:semantics>
+                                        
                                     </mml:math>
+                                    
                                 </imagedata>
+                                
                             </imageobject>
+                            
                         </inlinemediaobject>
+                        
                         (サブ区間について)
+                        
                     </para>
+                    
                     <para>
+                        
                         <inlinemediaobject>
+                            
                             <imageobject>
+                                
                                 <imagedata>
+                                    
                                     <mml:math>
+                                        
                                         <mml:semantics>
+                                            
                                             <mml:mi>v</mml:mi>
+                                            
                                         </mml:semantics>
+                                        
                                     </mml:math>
+                                    
                                 </imagedata>
+                                
                             </imageobject>
+                            
                         </inlinemediaobject>
+                        
                         が近似解ベクトルの場合,
+                        
                         <inlinemediaobject>
+                            
                             <imageobject>
+                                
                                 <imagedata>
+                                    
                                     <mml:math>
+                                        
                                         <mml:semantics>
+                                            
                                             <mml:mi>u</mml:mi>
+                                            
                                         </mml:semantics>
+                                        
                                     </mml:math>
+                                    
                                 </imagedata>
+                                
                             </imageobject>
+                            
                         </inlinemediaobject>
+                        
                         は厳密解(未知)となります.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>fixpnt</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         <literal>nfxpnt=ipar(11)</literal>次の配列. 
+                        
                         各メッシュに含まれる<literal>x_low</literal> および
+                        
                         <literal>x_up</literal>以外の点を含みます.
+                        
                         このコードは,<literal>x_low</literal> および <literal>x_up</literal>
+                        
                         以外の全ての周辺条件点(<literal>zeta</literal>の説明を参照)が
+                        
                         <literal>fixpnt</literal>の中の固定点として
+                        
                         含まれることを必要とします.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>fsub</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         <link linkend="external">external</link> は,以下の
+                        
                         列ベクトルの評価に使用されます. <literal>f=</literal>
+                        
                         <inlinemediaobject>
+                            
                             <imageobject>
+                                
                                 <imagedata>
+                                    
                                     <mml:math>
+                                        
                                         <mml:semantics>
+                                            
                                             <mml:mrow>
+                                                
                                                 <mml:mo mml:stretchy="false">[</mml:mo>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:msub>
+                                                        
                                                         <mml:mi>f</mml:mi><mml:mn>1</mml:mn>
+                                                        
                                                     </mml:msub>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:mo mml:stretchy="false">(</mml:mo>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mi>x</mml:mi><mml:mi>,</mml:mi><mml:mi>z</mml:mi>
+                                                            
                                                             <mml:mrow>
+                                                                
                                                                 <mml:mo mml:stretchy="false">(</mml:mo>
+                                                                
                                                                 <mml:mrow>
+                                                                    
                                                                     <mml:mi>u</mml:mi>
+                                                                    
                                                                     <mml:mrow>
+                                                                        
                                                                         <mml:mo mml:stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo mml:stretchy="false">)</mml:mo>
+                                                                        
                                                                     </mml:mrow>
+                                                                    
                                                                 </mml:mrow>
+                                                                
                                                                 <mml:mo mml:stretchy="false">)</mml:mo>
+                                                                
                                                             </mml:mrow>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                         <mml:mo mml:stretchy="false">)</mml:mo>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                     <mml:mi>;</mml:mi>
+                                                    
                                                     <mml:msub>
+                                                        
                                                         <mml:mi>f</mml:mi><mml:mn>2</mml:mn>
+                                                        
                                                     </mml:msub>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:mo mml:stretchy="false">(</mml:mo>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mi>x</mml:mi><mml:mi>,</mml:mi><mml:mi>z</mml:mi>
+                                                            
                                                             <mml:mrow>
+                                                                
                                                                 <mml:mo mml:stretchy="false">(</mml:mo>
+                                                                
                                                                 <mml:mrow>
+                                                                    
                                                                     <mml:mi>u</mml:mi>
+                                                                    
                                                                     <mml:mrow>
+                                                                        
                                                                         <mml:mo mml:stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo mml:stretchy="false">)</mml:mo>
+                                                                        
                                                                     </mml:mrow>
+                                                                    
                                                                 </mml:mrow>
+                                                                
                                                                 <mml:mo mml:stretchy="false">)</mml:mo>
+                                                                
                                                             </mml:mrow>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                         <mml:mo mml:stretchy="false">)</mml:mo>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                     <mml:mi>,</mml:mi><mml:mo mml:stretchy="false">⋯</mml:mo><mml:mi>,</mml:mi>
+                                                    
                                                     <mml:msub>
+                                                        
                                                         <mml:mi>f</mml:mi><mml:mi>N</mml:mi>
+                                                        
                                                     </mml:msub>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:mo mml:stretchy="false">(</mml:mo>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mi>x</mml:mi><mml:mi>,</mml:mi><mml:mi>z</mml:mi>
+                                                            
                                                             <mml:mrow>
+                                                                
                                                                 <mml:mo mml:stretchy="false">(</mml:mo>
+                                                                
                                                                 <mml:mrow>
+                                                                    
                                                                     <mml:mi>u</mml:mi>
+                                                                    
                                                                     <mml:mrow>
+                                                                        
                                                                         <mml:mo mml:stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo mml:stretchy="false">)</mml:mo>
+                                                                        
                                                                     </mml:mrow>
+                                                                    
                                                                 </mml:mrow>
+                                                                
                                                                 <mml:mo mml:stretchy="false">)</mml:mo>
+                                                                
                                                             </mml:mrow>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                         <mml:mo mml:stretchy="false">)</mml:mo>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                 </mml:mrow>
+                                                
                                                 <mml:mo mml:stretchy="false">]</mml:mo>
+                                                
                                             </mml:mrow>
+                                            
                                             <mml:annotation mml:encoding="StarMath 5.0">[f_1(x,z(u(x)));
+                                                
                                                 f_2(x,z(u(x))),dotsaxis,
+                                                
                                                 f_N(x,z(u(x)))]
+                                                
                                             </mml:annotation>
+                                            
                                         </mml:semantics>
+                                        
                                     </mml:math>
+                                    
                                 </imagedata>
+                                
                             </imageobject>
+                            
                         </inlinemediaobject>
+                        
+                        
+                        
                         ただし,
+                        
                         <literal>x_low</literal> &lt;= <literal>x</literal> &lt;= <literal>x_up</literal> の任意の<literal>x</literal>,
+                        
                         および <literal>z=z(u(x))</literal> となる任意の<literal>z</literal> とします.
+                        
                         (以下の説明を参照)
+                        
                     </para>
+                    
                     <para>外部関数は以下のように宣言を必要とします:</para>
+                    
                     <itemizedlist>
+                        
                         <listitem>
+                            
                             <para>Fortranの場合, 呼び出し手順を以下のようにします:</para>
+                            
                             <programlisting role="no-scilab-exec"><![CDATA[  
 subroutine fsub(x,zu,f)
 double precision zu(*), f(*),x 
  ]]></programlisting>
+                            
                         </listitem>
+                        
                         <listitem>
+                            
                             <para>Cの場合,関数プロトタイプを以下のようにします:</para>
+                            
                             <programlisting role="no-scilab-exec"><![CDATA[  
 void fsub(double *x, double *zu, double *f)
  ]]></programlisting>
+                            
                         </listitem>
+                        
                         <listitem>
+                            
                             <para>そしてScilab上では:</para>
+                            
                             <programlisting role="no-scilab-exec"><![CDATA[  
 function f=fsub(x,zu,parameters)
  ]]></programlisting>
+                            
                         </listitem>
+                        
                     </itemizedlist>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>dfsub</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         <link linkend="external">external</link>は,
+                        
                         点<literal>x</literal>におけるヤコビアン<literal>f(x,z(u))</literal>の
+                        
                         評価に使用されます.
+                        
                         ただし,<literal>z(u(x))</literal>は,
+                        
                         <literal>fsub</literal>と同様に定義され,
+                        
                         <literal>N</literal> 行 <literal>M</literal>列配列
+                        
                         dfには,<literal>f</literal>の偏微分が代入されます:
+                        
                     </para>
+                    
                     <informalequation>
+                        
                         <mediaobject>
+                            
                             <imageobject>
+                                
                                 <imagedata align="center">
+                                    
                                     <mml:math>
+                                        
                                         <mml:semantics>
+                                            
                                             <mml:mrow>
+                                                
                                                 <mml:mi mml:fontstyle="italic">df</mml:mi>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:mo mml:stretchy="false">(</mml:mo>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mi>i</mml:mi>
+                                                            
                                                             <mml:mi>,</mml:mi>
+                                                            
                                                             <mml:mi>j</mml:mi>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                         <mml:mo mml:stretchy="false">)</mml:mo>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                     <mml:mo mml:stretchy="false">=</mml:mo>
+                                                    
                                                     <mml:mfrac>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">∂</mml:mo>
+                                                            
                                                             <mml:msub>
+                                                                
                                                                 <mml:mi>f</mml:mi>
+                                                                
                                                                 <mml:mi>i</mml:mi>
+                                                                
                                                             </mml:msub>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">∂</mml:mo>
+                                                            
                                                             <mml:msub>
+                                                                
                                                                 <mml:mi>z</mml:mi>
+                                                                
                                                                 <mml:mi>j</mml:mi>
+                                                                
                                                             </mml:msub>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                     </mml:mfrac>
+                                                    
                                                 </mml:mrow>
+                                                
                                                 <mml:mtext> for
+                                                    
                                                 </mml:mtext>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mo mml:stretchy="true">{</mml:mo>
+                                                    
                                                     <mml:mtable>
+                                                        
                                                         <mml:mtr>
+                                                            
                                                             <mml:mrow>
+                                                                
                                                                 <mml:mrow>
+                                                                    
                                                                     <mml:mi>i</mml:mi>
+                                                                    
                                                                     <mml:mo mml:stretchy="false">=</mml:mo>
+                                                                    
                                                                     <mml:mn>1</mml:mn>
+                                                                    
                                                                 </mml:mrow>
+                                                                
                                                                 <mml:mi mml:fontstyle="normal">:</mml:mi>
+                                                                
                                                                 <mml:mi mml:fontstyle="italic">N</mml:mi>
+                                                                
                                                             </mml:mrow>
+                                                            
                                                         </mml:mtr>
+                                                        
                                                         <mml:mtr>
+                                                            
                                                             <mml:mrow>
+                                                                
                                                                 <mml:mrow>
+                                                                    
                                                                     <mml:mi>j</mml:mi>
+                                                                    
                                                                     <mml:mo mml:stretchy="false">=</mml:mo>
+                                                                    
                                                                     <mml:mn>1</mml:mn>
+                                                                    
                                                                 </mml:mrow>
+                                                                
                                                                 <mml:mi mml:fontstyle="normal">:</mml:mi>
+                                                                
                                                                 <mml:mi mml:fontstyle="italic">M</mml:mi>
+                                                                
                                                             </mml:mrow>
+                                                            
                                                         </mml:mtr>
+                                                        
                                                     </mml:mtable>
+                                                    
                                                 </mml:mrow>
+                                                
                                             </mml:mrow>
+                                            
                                             <mml:annotation mml:encoding="StarMath 5.0">df(i,j)= {partial{f_i}} over
+                                                
                                                 {partial{z_j}} ~ for ~ left lbrace binom{i=1:N}{j=1:M} right
+                                                
                                                 none
+                                                
                                             </mml:annotation>
+                                            
                                         </mml:semantics>
+                                        
                                     </mml:math>
+                                    
                                 </imagedata>
+                                
                             </imageobject>
+                            
                         </mediaobject>
+                        
                     </informalequation>
+                    
                     <para>外部関数は以下のように宣言を必要とします:</para>
+                    
                     <itemizedlist>
+                        
                         <listitem>
+                            
                             <para>Fortranの場合, 呼び出し手順を以下のようにします:</para>
+                            
                             <programlisting role="no-scilab-exec"><![CDATA[  
 subroutine dfsub(x,zu,df)
 double precision zu(*), df(*),x
  ]]></programlisting>
+                            
                         </listitem>
+                        
                         <listitem>
+                            
                             <para>Cの場合, 関数プロトタイプを以下のようにします:</para>
+                            
                             <programlisting role="no-scilab-exec"><![CDATA[  
 void dfsub(double *x, double *zu, double *df)
  ]]></programlisting>
+                            
                         </listitem>
+                        
                         <listitem>
+                            
                             <para>そして,Scilabにおいては:</para>
+                            
                             <programlisting role="no-scilab-exec"><![CDATA[  
 function df=dfsub(x,zu,parameters)
  ]]></programlisting>
+                            
                         </listitem>
+                        
                     </itemizedlist>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>gsub</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         以下の評価に使用される<link linkend="external">external</link>
+                        
                         <inlinemediaobject>
+                            
                             <imageobject>
+                                
                                 <imagedata>
+                                    
                                     <mml:math>
+                                        
                                         <mml:semantics>
+                                            
                                             <mml:mrow>
+                                                
                                                 <mml:msub>
+                                                    
                                                     <mml:mi>g</mml:mi><mml:mi>i</mml:mi>
+                                                    
                                                 </mml:msub>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mo mml:stretchy="false">(</mml:mo>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:msub>
+                                                            
                                                             <mml:mo mml:stretchy="false">ζ</mml:mo><mml:mi>i</mml:mi>
+                                                            
                                                         </mml:msub>
+                                                        
                                                         <mml:mi>,</mml:mi><mml:mi>z</mml:mi>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">(</mml:mo>
+                                                            
                                                             <mml:mrow>
+                                                                
                                                                 <mml:mi>u</mml:mi>
+                                                                
                                                                 <mml:mrow>
+                                                                    
                                                                     <mml:mo mml:stretchy="false">(</mml:mo>
+                                                                    
                                                                     <mml:msub>
+                                                                        
                                                                         <mml:mo mml:stretchy="false">ζ</mml:mo><mml:mi>i</mml:mi>
+                                                                        
                                                                     </mml:msub>
+                                                                    
                                                                     <mml:mo mml:stretchy="false">)</mml:mo>
+                                                                    
                                                                 </mml:mrow>
+                                                                
                                                             </mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">)</mml:mo>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                     <mml:mo mml:stretchy="false">)</mml:mo>
+                                                    
                                                 </mml:mrow>
+                                                
                                             </mml:mrow>
+                                            
                                             <mml:annotation mml:encoding="StarMath 5.0">g_i(%zeta_i,z(u(%zeta_i)))</mml:annotation>
+                                            
                                         </mml:semantics>
+                                        
                                     </mml:math>
+                                    
                                 </imagedata>
+                                
                             </imageobject>
+                            
                         </inlinemediaobject>
+                        
                         given z=
+                        
                         <inlinemediaobject>
+                            
                             <imageobject>
+                                
                                 <imagedata>
+                                    
                                     <mml:math>
+                                        
                                         <mml:semantics>
+                                            
                                             <mml:mrow>
+                                                
                                                 <mml:mi>z</mml:mi>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mo mml:stretchy="false">(</mml:mo>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:mi>u</mml:mi>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">(</mml:mo>
+                                                            
                                                             <mml:msub>
+                                                                
                                                                 <mml:mo mml:stretchy="false">ζ</mml:mo><mml:mi>i</mml:mi>
+                                                                
                                                             </mml:msub>
+                                                            
                                                             <mml:mo mml:stretchy="false">)</mml:mo>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                     <mml:mo mml:stretchy="false">)</mml:mo>
+                                                    
                                                 </mml:mrow>
+                                                
                                             </mml:mrow>
+                                            
                                             <mml:annotation mml:encoding="StarMath 5.0">z(u(%zeta_i))</mml:annotation>
+                                            
                                         </mml:semantics>
+                                        
                                     </mml:math>
+                                    
                                 </imagedata>
+                                
                             </imageobject>
+                            
                         </inlinemediaobject>
+                        
+                        
+                        
                         <literal>z = zeta(i)</literal> ただし,
+                        
                         <literal>1&lt;=i&lt;=M.</literal>
+                        
                     </para>
+                    
                     <para>外部関数は以下のように宣言を必要とします:</para>
+                    
                     <itemizedlist>
+                        
                         <listitem>
+                            
                             <para>Fortranの場合, 呼び出し手順を以下のようにします:</para>
+                            
                             <programlisting role="no-scilab-exec"><![CDATA[  
 subroutine gsub(i,zu,g)
 double precision zu(*), g(*)
 integer i
  ]]></programlisting>
+                            
                         </listitem>
+                        
                         <listitem>
+                            
                             <para>Cの場合, 関数プロトタイプを以下のようにします:</para>
+                            
                             <programlisting role="no-scilab-exec"><![CDATA[  
 void gsub(int *i, double *zu, double *g)
  ]]></programlisting>
+                            
                         </listitem>
+                        
                         <listitem>
+                            
                             <para>そして,Scilabでは:</para>
+                            
                             <programlisting role="no-scilab-exec"><![CDATA[  
 function g=gsub(i,zu,parameters)
  ]]></programlisting>
+                            
                             <para>
+                                
                                 <literal>fsub</literal>の<literal>f</literal>とは逆に
+                                
                                 <literal>g</literal>では
+                                
                                 コール毎に一つの値のみが返されることに注意してください.
+                                
                             </para>
+                            
                         </listitem>
+                        
                     </itemizedlist>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>dgsub</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         an <link linkend="external">external</link> used to evaluate
+                        
                         the <literal>i</literal>-th row of the Jacobian of <literal>g(x,u(x))</literal>. Where
+                        
                         <literal>z(u)</literal> is as for <literal>fsub</literal>, <literal>i</literal> as for 
+                        
                         <literal>gsub</literal> and the <literal>M</literal>-vector <literal>dg</literal> should 
+                        
                         be filled with the partial derivatives of <literal>g</literal>, viz, for a particular call one 
+                        
                         calculates
+                        
                     </para>
+                    
                     <informalequation>
+                        
                         <mediaobject>
+                            
                             <imageobject>
+                                
                                 <imagedata align="center">
+                                    
                                     <mml:math>
+                                        
                                         <mml:semantics>
+                                            
                                             <mml:mrow>
+                                                
                                                 <mml:mi mml:fontstyle="italic">dg</mml:mi>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:mo mml:stretchy="false">(</mml:mo>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mi>i</mml:mi>
+                                                            
                                                             <mml:mi>,</mml:mi>
+                                                            
                                                             <mml:mi>j</mml:mi>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                         <mml:mo mml:stretchy="false">)</mml:mo>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                     <mml:mo mml:stretchy="false">=</mml:mo>
+                                                    
                                                     <mml:mfrac>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">∂</mml:mo>
+                                                            
                                                             <mml:msub>
+                                                                
                                                                 <mml:mi>g</mml:mi>
+                                                                
                                                                 <mml:mi>i</mml:mi>
+                                                                
                                                             </mml:msub>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">∂</mml:mo>
+                                                            
                                                             <mml:msub>
+                                                                
                                                                 <mml:mi>z</mml:mi>
+                                                                
                                                                 <mml:mi>j</mml:mi>
+                                                                
                                                             </mml:msub>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                     </mml:mfrac>
+                                                    
                                                 </mml:mrow>
+                                                
                                                 <mml:mtext> for
+                                                    
                                                 </mml:mtext>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mo mml:stretchy="true">{</mml:mo>
+                                                    
                                                     <mml:mtable>
+                                                        
                                                         <mml:mtr>
+                                                            
                                                             <mml:mrow>
+                                                                
                                                                 <mml:mrow>
+                                                                    
                                                                     <mml:mi>i</mml:mi>
+                                                                    
                                                                     <mml:mo mml:stretchy="false">=</mml:mo>
+                                                                    
                                                                     <mml:mn>1</mml:mn>
+                                                                    
                                                                 </mml:mrow>
+                                                                
                                                                 <mml:mi mml:fontstyle="normal">:</mml:mi>
+                                                                
                                                                 <mml:mi mml:fontstyle="italic">M</mml:mi>
+                                                                
                                                             </mml:mrow>
+                                                            
                                                         </mml:mtr>
+                                                        
                                                         <mml:mtr>
+                                                            
                                                             <mml:mrow>
+                                                                
                                                                 <mml:mrow>
+                                                                    
                                                                     <mml:mi>j</mml:mi>
+                                                                    
                                                                     <mml:mo mml:stretchy="false">=</mml:mo>
+                                                                    
                                                                     <mml:mn>1</mml:mn>
+                                                                    
                                                                 </mml:mrow>
+                                                                
                                                                 <mml:mi mml:fontstyle="normal">:</mml:mi>
+                                                                
                                                                 <mml:mi mml:fontstyle="italic">M</mml:mi>
+                                                                
                                                             </mml:mrow>
+                                                            
                                                         </mml:mtr>
+                                                        
                                                     </mml:mtable>
+                                                    
                                                 </mml:mrow>
+                                                
                                             </mml:mrow>
+                                            
                                             <mml:annotation mml:encoding="StarMath 5.0">dg(i,j)= {partial{g_i}} over
+                                                
                                                 {partial{z_j}} ~ for ~ left lbrace binom{i=1:M}{j=1:M} right
+                                                
                                                 none
+                                                
                                             </mml:annotation>
+                                            
                                         </mml:semantics>
+                                        
                                     </mml:math>
+                                    
                                 </imagedata>
+                                
                             </imageobject>
+                            
                         </mediaobject>
+                        
                     </informalequation>
+                    
                     <para>外部関数は以下のような宣言を必要とします:</para>
+                    
                     <itemizedlist>
+                        
                         <listitem>
+                            
                             <para>Fortranの場合, 呼び出し手順を以下のようにします:</para>
+                            
                             <programlisting role="no-scilab-exec"><![CDATA[  
 subroutine dgsub(i,zu,dg)
 double precision zu(*), dg(*)
  ]]></programlisting>
+                            
                         </listitem>
+                        
                         <listitem>
+                            
                             <para>Cの場合, 関数プロトタイプを以下のようにします:</para>
+                            
                             <programlisting role="no-scilab-exec"><![CDATA[  
 void dgsub(int *i, double *zu, double *dg)
  ]]></programlisting>
+                            
                         </listitem>
+                        
                         <listitem>
+                            
                             <para>そして,Scilabでは:</para>
+                            
                             <programlisting role="no-scilab-exec"><![CDATA[  
 function dg=dgsub(i,zu,parameters)
  ]]></programlisting>
+                            
                         </listitem>
+                        
                     </itemizedlist>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>guess</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         <literal>z(u(x))</literal>および
+                        
                         <literal>u(x)</literal>の<literal>mj</literal>階微分<literal>dmval(u(x))</literal>
+                        
                         の初期近似値を見積もるために
+                        
                         <link linkend="external">external</link>が使用されます.
+                        
                         <literal>ipar(9) = 1</literal>の場合のみ, このサブルーチンが
+                        
                         使用されることに注意してください.
+                        
                         このため,<literal>zu</literal>の<literal>M</literal>個の要素および <literal>dmval</literal> の <literal>N</literal>個の
+                        
                         要素が<literal>x_low</literal> &lt;= <literal>x</literal> &lt;= <literal>x_up</literal>の範囲の任意の <literal>x</literal> について計算される
+                        
                         必要があります.
+                        
                     </para>
+                    
                     <para>外部関数は以下のように宣言を必要とします:</para>
+                    
                     <itemizedlist>
+                        
                         <listitem>
+                            
                             <para>Fortranの場合, 呼び出し手順を以下のようにします:</para>
+                            
                             <programlisting role="no-scilab-exec"><![CDATA[  
 subroutine guess(x,zu,dmval)
 double precision x,z(*), dmval(*)
  ]]></programlisting>
+                            
                         </listitem>
+                        
                         <listitem>
+                            
                             <para>Cの場合, 関数プロトタイプを以下のようにします</para>
+                            
                             <programlisting role="no-scilab-exec"><![CDATA[  
 void fsub(double *x, double *zu, double *dmval)
  ]]></programlisting>
+                            
                         </listitem>
+                        
                         <listitem>
+                            
                             <para>そしてScilab上では, </para>
+                            
                             <programlisting role="no-scilab-exec"><![CDATA[  
 function [dmval,zu]=fsub(x,parameters)
  ]]></programlisting>
+                            
                         </listitem>
+                        
                     </itemizedlist>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>&lt;optional_args&gt;</term>
+                
                 <listitem>
+                    
                     <para>以下のどれかとする必要があります:</para>
+                    
                     <itemizedlist>
+                        
                         <listitem>
+                            
                             <para>
+                                
                                 以下の一連の値:
+                                
                                 <literal>guess, dfsub, dgsub, fixpnt, ndimf, ndimi, ltol, tol,
+                                    
                                     ntol,nonlin, collpnt, subint, iprint, ireg, ifail
+                                    
                                 </literal>
+                                
                             </para>
+                            
                         </listitem>
+                        
                         <listitem>
+                            
                             <para>
+                                
                                 もしくは,一連の<literal>arg_name=argvalue</literal>
+                                
                                 で指定します.
+                                
                                 ただし <literal>arg_name</literal> は以下のどれかとなります: 
+                                
                                 <literal>guess</literal>,
+                                
                                 <literal>dfsub</literal>, <literal>dgsub</literal>,
+                                
                                 <literal>fixpnt</literal>, <literal>ndimf</literal>,
+                                
                                 <literal>ndimi</literal>, <literal>ltol</literal>,
+                                
                                 <literal>tol</literal>, <literal>ntol</literal>,
+                                
                                 <literal>nonlin</literal>, <literal>collpnt</literal>,
+                                
                                 <literal>subint</literal>, <literal>iprint</literal>,
+                                
                                 <literal>ireg</literal>, <literal>ifail</literal>
+                                
                             </para>
+                            
                         </listitem>
+                        
                     </itemizedlist>
+                    
                     <para>
+                        
                         これらの引数が指定される場合は,常に
+                        
                         <literal>ifail</literal>は上記のように説明されます.
+                        
                         <literal>ifail</literal>は選択されたオプション引数
+                        
                         に対応する bvode コールを表示するために使用できます.
+                        
                         もし,<literal>guess</literal> が指定された場合,
+                        
                         <literal>iguess</literal>が 1 に設定されます.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             これらの関数は, 以下のように定義された ode-s の
+            
             混合次数に関連するシステム多点境界値問題を解きます.
+            
         </para>
+        
         <informalequation>
+            
             <mediaobject>
+                
                 <imageobject>
+                    
                     <imagedata align="left">
+                        
                         <mml:math>
+                            
                             <mml:semantics>
+                                
                                 <mml:mrow>
+                                    
                                     <mml:mo mml:stretchy="true">{</mml:mo>
+                                    
                                     <mml:mtable>
+                                        
                                         <mml:mtr>
+                                            
                                             <mml:mrow>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:msubsup>
+                                                        
                                                         <mml:mi>u</mml:mi>
+                                                        
                                                         <mml:mi>i</mml:mi>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">(</mml:mo>
+                                                            
                                                             <mml:msub>
+                                                                
                                                                 <mml:mi>m</mml:mi>
+                                                                
                                                                 <mml:mi>i</mml:mi>
+                                                                
                                                             </mml:msub>
+                                                            
                                                             <mml:mo mml:stretchy="false">)</mml:mo>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                     </mml:msubsup>
+                                                    
                                                     <mml:mo mml:stretchy="false">=</mml:mo>
+                                                    
                                                     <mml:msub>
+                                                        
                                                         <mml:mi>f</mml:mi>
+                                                        
                                                         <mml:mi>i</mml:mi>
+                                                        
                                                     </mml:msub>
+                                                    
                                                 </mml:mrow>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mo mml:stretchy="false">(</mml:mo>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:mi>x</mml:mi>
+                                                        
                                                         <mml:mi>,</mml:mi>
+                                                        
                                                         <mml:mi>z</mml:mi>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">(</mml:mo>
+                                                            
                                                             <mml:mrow>
+                                                                
                                                                 <mml:mi>u</mml:mi>
+                                                                
                                                                 <mml:mrow>
+                                                                    
                                                                     <mml:mo mml:stretchy="false">(</mml:mo>
+                                                                    
                                                                     <mml:mi>x</mml:mi>
+                                                                    
                                                                     <mml:mo mml:stretchy="false">)</mml:mo>
+                                                                    
                                                                 </mml:mrow>
+                                                                
                                                             </mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">)</mml:mo>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                     <mml:mo mml:stretchy="false">)</mml:mo>
+                                                    
                                                 </mml:mrow>
+                                                
                                                 <mml:mi/>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mo mml:stretchy="true">{</mml:mo>
+                                                    
                                                     <mml:mtable>
+                                                        
                                                         <mml:mtr>
+                                                            
                                                             <mml:mrow>
+                                                                
                                                                 <mml:mrow>
+                                                                    
                                                                     <mml:mi>i</mml:mi>
+                                                                    
                                                                     <mml:mo mml:stretchy="false">=</mml:mo>
+                                                                    
                                                                     <mml:mn>1</mml:mn>
+                                                                    
                                                                 </mml:mrow>
+                                                                
                                                                 <mml:mi mml:fontstyle="normal">:</mml:mi>
+                                                                
                                                                 <mml:mi>N</mml:mi>
+                                                                
                                                             </mml:mrow>
+                                                            
                                                         </mml:mtr>
+                                                        
                                                         <mml:mtr>
+                                                            
                                                             <mml:mrow>
+                                                                
                                                                 <mml:mi>x</mml:mi>
+                                                                
                                                                 <mml:mo mml:stretchy="false">∈</mml:mo>
+                                                                
                                                                 <mml:mfenced mml:close="[" mml:open="]">
+                                                                    
                                                                     <mml:mrow>
+                                                                        
                                                                         <mml:msub>
+                                                                            
                                                                             <mml:mi>x</mml:mi>
+                                                                            
                                                                             <mml:mi>l</mml:mi>
+                                                                            
                                                                         </mml:msub>
+                                                                        
                                                                         <mml:mi>,</mml:mi>
+                                                                        
                                                                         <mml:msub>
+                                                                            
                                                                             <mml:mi>x</mml:mi>
+                                                                            
                                                                             <mml:mi>u</mml:mi>
+                                                                            
                                                                         </mml:msub>
+                                                                        
                                                                     </mml:mrow>
+                                                                    
                                                                 </mml:mfenced>
+                                                                
                                                             </mml:mrow>
+                                                            
                                                         </mml:mtr>
+                                                        
                                                     </mml:mtable>
+                                                    
                                                 </mml:mrow>
+                                                
                                             </mml:mrow>
+                                            
                                         </mml:mtr>
+                                        
                                         <mml:mtr>
+                                            
                                             <mml:mi/>
+                                            
                                         </mml:mtr>
+                                        
                                         <mml:mtr>
+                                            
                                             <mml:mrow>
+                                                
                                                 <mml:msub>
+                                                    
                                                     <mml:mi>g</mml:mi>
+                                                    
                                                     <mml:mi>j</mml:mi>
+                                                    
                                                 </mml:msub>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:mo mml:stretchy="false">(</mml:mo>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:msub>
+                                                                
                                                                 <mml:mo mml:stretchy="false">ζ</mml:mo>
+                                                                
                                                                 <mml:mi>j</mml:mi>
+                                                                
                                                             </mml:msub>
+                                                            
                                                             <mml:mi>,</mml:mi>
+                                                            
                                                             <mml:mi>z</mml:mi>
+                                                            
                                                             <mml:mrow>
+                                                                
                                                                 <mml:mo mml:stretchy="false">(</mml:mo>
+                                                                
                                                                 <mml:mrow>
+                                                                    
                                                                     <mml:mi>u</mml:mi>
+                                                                    
                                                                     <mml:mrow>
+                                                                        
                                                                         <mml:mo mml:stretchy="false">(</mml:mo>
+                                                                        
                                                                         <mml:msub>
+                                                                            
                                                                             <mml:mo mml:stretchy="false">ζ</mml:mo>
+                                                                            
                                                                             <mml:mi>j</mml:mi>
+                                                                            
                                                                         </mml:msub>
+                                                                        
                                                                         <mml:mo mml:stretchy="false">)</mml:mo>
+                                                                        
                                                                     </mml:mrow>
+                                                                    
                                                                 </mml:mrow>
+                                                                
                                                                 <mml:mo mml:stretchy="false">)</mml:mo>
+                                                                
                                                             </mml:mrow>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                         <mml:mo mml:stretchy="false">)</mml:mo>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                     <mml:mo mml:stretchy="false">=</mml:mo>
+                                                    
                                                     <mml:mn>0</mml:mn>
+                                                    
                                                 </mml:mrow>
+                                                
                                                 <mml:mi/>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mtext>,</mml:mtext>
+                                                    
                                                     <mml:mi>j</mml:mi>
+                                                    
                                                     <mml:mo mml:stretchy="false">=</mml:mo>
+                                                    
                                                     <mml:mn>1</mml:mn>
+                                                    
                                                 </mml:mrow>
+                                                
                                                 <mml:mi mml:fontstyle="normal">:</mml:mi>
+                                                
                                                 <mml:mi>M</mml:mi>
+                                                
                                             </mml:mrow>
+                                            
                                         </mml:mtr>
+                                        
                                     </mml:mtable>
+                                    
                                 </mml:mrow>
+                                
                                 <mml:annotation mml:encoding="StarMath 5.0">left lbrace
+                                    
                                     stack{u_i^(m_i)=f_i(x,z(u(x))) ~~left lbrace { binom{i=1:N}{x
+                                    
                                     in left ] a_l, a_u right [} } right none# `#
+                                    
                                     g_j(%zeta_j,z(u(%zeta_j))) = 0~~j=1:M} right
+                                    
                                     none
+                                    
                                 </mml:annotation>
+                                
                             </mml:semantics>
+                            
                         </mml:math>
+                        
                     </imagedata>
+                    
                 </imageobject>
+                
             </mediaobject>
+            
         </informalequation>
+        
         <para>ただし,e</para>
+        
         <mediaobject>
+            
             <imageobject>
+                
                 <imagedata align="left">
+                    
                     <mml:math>
+                        
                         <mml:semantics>
+                            
                             <mml:mrow>
+                                
                                 <mml:mo mml:stretchy="true">{</mml:mo>
+                                
                                 <mml:mtable>
+                                    
                                     <mml:mtr>
+                                        
                                         <mml:mrow>
+                                            
                                             <mml:mi>M</mml:mi>
+                                            
                                             <mml:mo mml:stretchy="false">=</mml:mo>
+                                            
                                             <mml:mrow>
+                                                
                                                 <mml:munderover>
+                                                    
                                                     <mml:mo mml:stretchy="false">∑</mml:mo>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:mi>i</mml:mi>
+                                                        
                                                         <mml:mo mml:stretchy="false">=</mml:mo>
+                                                        
                                                         <mml:mn>1</mml:mn>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                     <mml:mi>N</mml:mi>
+                                                    
                                                 </mml:munderover>
+                                                
                                                 <mml:msub>
+                                                    
                                                     <mml:mi>m</mml:mi>
+                                                    
                                                     <mml:mi>i</mml:mi>
+                                                    
                                                 </mml:msub>
+                                                
                                             </mml:mrow>
+                                            
                                         </mml:mrow>
+                                        
                                     </mml:mtr>
+                                    
                                     <mml:mtr>
+                                        
                                         <mml:mi/>
+                                        
                                     </mml:mtr>
+                                    
                                     <mml:mtr>
+                                        
                                         <mml:mrow>
+                                            
                                             <mml:mi>z</mml:mi>
+                                            
                                             <mml:mrow>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mo mml:stretchy="false">(</mml:mo>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:mi>u</mml:mi>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">(</mml:mo>
+                                                            
                                                             <mml:mi>x</mml:mi>
+                                                            
                                                             <mml:mo mml:stretchy="false">)</mml:mo>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                     <mml:mo mml:stretchy="false">)</mml:mo>
+                                                    
                                                 </mml:mrow>
+                                                
                                                 <mml:mo mml:stretchy="false">=</mml:mo>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mo mml:stretchy="false">[</mml:mo>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:msub>
+                                                            
                                                             <mml:mi>u</mml:mi>
+                                                            
                                                             <mml:mn>1</mml:mn>
+                                                            
                                                         </mml:msub>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">(</mml:mo>
+                                                            
                                                             <mml:mi>x</mml:mi>
+                                                            
                                                             <mml:mo mml:stretchy="false">)</mml:mo>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                         <mml:mi>;</mml:mi>
+                                                        
                                                         <mml:msubsup>
+                                                            
                                                             <mml:mi>u</mml:mi>
+                                                            
                                                             <mml:mn>1</mml:mn>
+                                                            
                                                             <mml:mn>1</mml:mn>
+                                                            
                                                         </mml:msubsup>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">(</mml:mo>
+                                                            
                                                             <mml:mi>x</mml:mi>
+                                                            
                                                             <mml:mo mml:stretchy="false">)</mml:mo>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                         <mml:mi>;</mml:mi>
+                                                        
                                                         <mml:mo mml:stretchy="false">⋯</mml:mo>
+                                                        
                                                         <mml:msubsup>
+                                                            
                                                             <mml:mi>u</mml:mi>
+                                                            
                                                             <mml:mn>1</mml:mn>
+                                                            
                                                             <mml:mrow>
+                                                                
                                                                 <mml:mo mml:stretchy="false">(</mml:mo>
+                                                                
                                                                 <mml:mrow>
+                                                                    
                                                                     <mml:msub>
+                                                                        
                                                                         <mml:mi>m</mml:mi>
+                                                                        
                                                                         <mml:mn>1</mml:mn>
+                                                                        
                                                                     </mml:msub>
+                                                                    
                                                                     <mml:mo mml:stretchy="false">−</mml:mo>
+                                                                    
                                                                     <mml:mn>1</mml:mn>
+                                                                    
                                                                 </mml:mrow>
+                                                                
                                                                 <mml:mo mml:stretchy="false">)</mml:mo>
+                                                                
                                                             </mml:mrow>
+                                                            
                                                         </mml:msubsup>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">(</mml:mo>
+                                                            
                                                             <mml:mi>x</mml:mi>
+                                                            
                                                             <mml:mo mml:stretchy="false">)</mml:mo>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                         <mml:mi>;</mml:mi>
+                                                        
                                                         <mml:mi/>
+                                                        
                                                         <mml:mo mml:stretchy="false">⋯</mml:mo>
+                                                        
                                                         <mml:mi>;</mml:mi>
+                                                        
                                                         <mml:mi/>
+                                                        
                                                         <mml:msub>
+                                                            
                                                             <mml:mi>u</mml:mi>
+                                                            
                                                             <mml:mi>N</mml:mi>
+                                                            
                                                         </mml:msub>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">(</mml:mo>
+                                                            
                                                             <mml:mi>x</mml:mi>
+                                                            
                                                             <mml:mo mml:stretchy="false">)</mml:mo>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                         <mml:mi>;</mml:mi>
+                                                        
                                                         <mml:msubsup>
+                                                            
                                                             <mml:mi>u</mml:mi>
+                                                            
                                                             <mml:mi>N</mml:mi>
+                                                            
                                                             <mml:mn>1</mml:mn>
+                                                            
                                                         </mml:msubsup>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">(</mml:mo>
+                                                            
                                                             <mml:mi>x</mml:mi>
+                                                            
                                                             <mml:mo mml:stretchy="false">)</mml:mo>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                         <mml:mi>;</mml:mi>
+                                                        
                                                         <mml:mo mml:stretchy="false">⋯</mml:mo>
+                                                        
                                                         <mml:mi>;</mml:mi>
+                                                        
                                                         <mml:msubsup>
+                                                            
                                                             <mml:mi>u</mml:mi>
+                                                            
                                                             <mml:mi>N</mml:mi>
+                                                            
                                                             <mml:mrow>
+                                                                
                                                                 <mml:mo mml:stretchy="false">(</mml:mo>
+                                                                
                                                                 <mml:mrow>
+                                                                    
                                                                     <mml:msub>
+                                                                        
                                                                         <mml:mi>m</mml:mi>
+                                                                        
                                                                         <mml:mi>N</mml:mi>
+                                                                        
                                                                     </mml:msub>
+                                                                    
                                                                     <mml:mo mml:stretchy="false">−</mml:mo>
+                                                                    
                                                                     <mml:mn>1</mml:mn>
+                                                                    
                                                                 </mml:mrow>
+                                                                
                                                                 <mml:mo mml:stretchy="false">)</mml:mo>
+                                                                
                                                             </mml:mrow>
+                                                            
                                                         </mml:msubsup>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">(</mml:mo>
+                                                            
                                                             <mml:mi>x</mml:mi>
+                                                            
                                                             <mml:mo mml:stretchy="false">)</mml:mo>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                     <mml:mo mml:stretchy="false">]</mml:mo>
+                                                    
                                                 </mml:mrow>
+                                                
                                             </mml:mrow>
+                                            
                                         </mml:mrow>
+                                        
                                     </mml:mtr>
+                                    
                                     <mml:mtr>
+                                        
                                         <mml:mi/>
+                                        
                                     </mml:mtr>
+                                    
                                     <mml:mtr>
+                                        
                                         <mml:mrow>
+                                            
                                             <mml:mrow>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:msub>
+                                                            
                                                             <mml:mi>x</mml:mi>
+                                                            
                                                             <mml:mi>l</mml:mi>
+                                                            
                                                         </mml:msub>
+                                                        
                                                         <mml:mo mml:stretchy="false">≤</mml:mo>
+                                                        
                                                         <mml:msub>
+                                                            
                                                             <mml:mo mml:stretchy="false">ζ</mml:mo>
+                                                            
                                                             <mml:mn>1</mml:mn>
+                                                            
                                                         </mml:msub>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                     <mml:mo mml:stretchy="false">≤</mml:mo>
+                                                    
                                                     <mml:mo mml:stretchy="false">⋯</mml:mo>
+                                                    
                                                 </mml:mrow>
+                                                
                                                 <mml:mo mml:stretchy="false">≤</mml:mo>
+                                                
                                                 <mml:msub>
+                                                    
                                                     <mml:mo mml:stretchy="false">ζ</mml:mo>
+                                                    
                                                     <mml:mi>M</mml:mi>
+                                                    
                                                 </mml:msub>
+                                                
                                             </mml:mrow>
+                                            
                                             <mml:mo mml:stretchy="false">≤</mml:mo>
+                                            
                                             <mml:msub>
+                                                
                                                 <mml:mi>x</mml:mi>
+                                                
                                                 <mml:mi>u</mml:mi>
+                                                
                                             </mml:msub>
+                                            
                                         </mml:mrow>
+                                        
                                     </mml:mtr>
+                                    
                                 </mml:mtable>
+                                
                             </mml:mrow>
+                            
                             <mml:annotation mml:encoding="StarMath 5.0">left lbrace stack
+                                
                                 { M= sum from {i=1} to {N} m_i # ~# z(u(x)) =
+                                
                                 [u_1(x);u_1^{1}(x);dotsaxis u_1^(m_1-1)(x);~ dotsaxis;
+                                
                                 ~u_N(x);u_N^{1}(x);dotsaxis; u_N^(m_N-1)(x)]# ~# x_l &lt;=
+                                
                                 %zeta_1 &lt;= dotsaxis &lt;= %zeta_M &lt;=x_u}right
+                                
                                 none
+                                
                             </mml:annotation>
+                            
                         </mml:semantics>
+                        
                     </mml:math>
+                    
                 </imagedata>
+                
             </imageobject>
+            
         </mediaobject>
+        
         <para>
+            
             外部関数で使用され, <literal>bvode</literal>  により返される
+            
             引数 <literal>zu</literal> は, 
+            
             指定した <literal>x</literal> に関する <literal>z(u(x))</literal>の要素により
+            
             構成される列ベクトルです.
+            
         </para>
+        
         <para>
+            
             解 u を近似するために使用される手法は,
+            
             ガウス点におけるコロケーションです.
+            
             この方法は,i番目(i = 1:N)の要素についてm(i)-1階の連続微分が可であることを
+            
             必要とします.
+            
             ここで, k はサブ区間毎のコロケーション点(ステージ)の数で,
+            
             <latex>k \ge \max\left(m(i)\right)</latex> となるように選択されます.
+            
             ルンゲクッタのノミナル解表現が使用されます.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <para>
+            
             最初の2つの問題は参考文献の論文 [1] からの引用です.
+            
         </para>
+        
         <itemizedlist>
+            
             <listitem>
+                
                 <para>
+                    
                     <emphasis role="bold">問題 1</emphasis> は
+                    
                     両端で単純支持され,均等に負荷がかかった剛性が可変の梁について
+                    
                     記述します.
+                    
                 </para>
+                
                 <para>以下のように定義することができます :</para>
+                
                 <para>次の4次の微分方程式を解きます:</para>
+                
                 <mediaobject>
+                    
                     <imageobject>
+                        
                         <imagedata align="left">
+                            
                             <mml:math>
+                                
                                 <mml:semantics>
+                                    
                                     <mml:mrow>
+                                        
                                         <mml:mfrac>
+                                            
                                             <mml:msup>
+                                                
                                                 <mml:mi>d</mml:mi>
+                                                
                                                 <mml:mn>4</mml:mn>
+                                                
                                             </mml:msup>
+                                            
                                             <mml:mrow>
+                                                
                                                 <mml:mi>d</mml:mi>
+                                                
                                                 <mml:msup>
+                                                    
                                                     <mml:mi>x</mml:mi>
+                                                    
                                                     <mml:mn>4</mml:mn>
+                                                    
                                                 </mml:msup>
+                                                
                                             </mml:mrow>
+                                            
                                         </mml:mfrac>
+                                        
                                         <mml:mi>u</mml:mi>
+                                        
                                         <mml:mrow>
+                                            
                                             <mml:mrow>
+                                                
                                                 <mml:mo mml:stretchy="false">(</mml:mo>
+                                                
                                                 <mml:mi>x</mml:mi>
+                                                
                                                 <mml:mo mml:stretchy="false">)</mml:mo>
+                                                
                                             </mml:mrow>
+                                            
                                             <mml:mo mml:stretchy="false">=</mml:mo>
+                                            
                                             <mml:mfrac>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:mn>1</mml:mn>
+                                                        
                                                         <mml:mo mml:stretchy="false">−</mml:mo>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mrow>
+                                                                
                                                                 <mml:mn>6</mml:mn>
+                                                                
                                                                 <mml:mo mml:stretchy="false">.</mml:mo>
+                                                                
                                                                 <mml:msup>
+                                                                    
                                                                     <mml:mi>x</mml:mi>
+                                                                    
                                                                     <mml:mn>2</mml:mn>
+                                                                    
                                                                 </mml:msup>
+                                                                
                                                             </mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">.</mml:mo>
+                                                            
                                                             <mml:mfrac>
+                                                                
                                                                 <mml:msup>
+                                                                    
                                                                     <mml:mi>d</mml:mi>
+                                                                    
                                                                     <mml:mn>3</mml:mn>
+                                                                    
                                                                 </mml:msup>
+                                                                
                                                                 <mml:mrow>
+                                                                    
                                                                     <mml:mi>d</mml:mi>
+                                                                    
                                                                     <mml:msup>
+                                                                        
                                                                         <mml:mi>x</mml:mi>
+                                                                        
                                                                         <mml:mn>3</mml:mn>
+                                                                        
                                                                     </mml:msup>
+                                                                    
                                                                 </mml:mrow>
+                                                                
                                                             </mml:mfrac>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                     <mml:mi>u</mml:mi>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">(</mml:mo>
+                                                            
                                                             <mml:mi>x</mml:mi>
+                                                            
                                                             <mml:mo mml:stretchy="false">)</mml:mo>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                         <mml:mo mml:stretchy="false">−</mml:mo>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mrow>
+                                                                
                                                                 <mml:mn>6</mml:mn>
+                                                                
                                                                 <mml:mo mml:stretchy="false">.</mml:mo>
+                                                                
                                                                 <mml:mi>x</mml:mi>
+                                                                
                                                             </mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">.</mml:mo>
+                                                            
                                                             <mml:mfrac>
+                                                                
                                                                 <mml:msup>
+                                                                    
                                                                     <mml:mi>d</mml:mi>
+                                                                    
                                                                     <mml:mn>2</mml:mn>
+                                                                    
                                                                 </mml:msup>
+                                                                
                                                                 <mml:mrow>
+                                                                    
                                                                     <mml:mi>d</mml:mi>
+                                                                    
                                                                     <mml:msup>
+                                                                        
                                                                         <mml:mi>x</mml:mi>
+                                                                        
                                                                         <mml:mn>2</mml:mn>
+                                                                        
                                                                     </mml:msup>
+                                                                    
                                                                 </mml:mrow>
+                                                                
                                                             </mml:mfrac>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                     <mml:mi>u</mml:mi>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:mo mml:stretchy="false">(</mml:mo>
+                                                        
                                                         <mml:mi>x</mml:mi>
+                                                        
                                                         <mml:mo mml:stretchy="false">)</mml:mo>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                 </mml:mrow>
+                                                
                                                 <mml:msup>
+                                                    
                                                     <mml:mi>x</mml:mi>
+                                                    
                                                     <mml:mn>3</mml:mn>
+                                                    
                                                 </mml:msup>
+                                                
                                             </mml:mfrac>
+                                            
                                         </mml:mrow>
+                                        
                                     </mml:mrow>
+                                    
                                     <mml:annotation mml:encoding="StarMath 5.0">d^4 over {d
+                                        
                                         x^4} u(x)={1 -6*x^2*{{d^3} over {d x^3}} u(x)-6*x*{{d^2}
+                                        
                                         over {d x^2}} u(x)} over x^3
+                                        
                                     </mml:annotation>
+                                    
                                 </mml:semantics>
+                                
                             </mml:math>
+                            
                         </imagedata>
+                        
                     </imageobject>
+                    
                 </mediaobject>
+                
                 <para>設定する境界条件:</para>
+                
                 <mediaobject>
+                    
                     <imageobject>
+                        
                         <imagedata align="left">
+                            
                             <mml:math>
+                                
                                 <mml:semantics>
+                                    
                                     <mml:mrow>
+                                        
                                         <mml:mo mml:stretchy="true">{</mml:mo>
+                                        
                                         <mml:mtable>
+                                            
                                             <mml:mtr>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mi>u</mml:mi>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">(</mml:mo>
+                                                            
                                                             <mml:mn>1</mml:mn>
+                                                            
                                                             <mml:mo mml:stretchy="false">)</mml:mo>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                         <mml:mo mml:stretchy="false">=</mml:mo>
+                                                        
                                                         <mml:mn>0</mml:mn>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                 </mml:mrow>
+                                                
                                             </mml:mtr>
+                                            
                                             <mml:mtr>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mfrac>
+                                                        
                                                         <mml:msup>
+                                                            
                                                             <mml:mi>d</mml:mi>
+                                                            
                                                             <mml:mn>2</mml:mn>
+                                                            
                                                         </mml:msup>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mi>d</mml:mi>
+                                                            
                                                             <mml:msup>
+                                                                
                                                                 <mml:mi>x</mml:mi>
+                                                                
                                                                 <mml:mn>2</mml:mn>
+                                                                
                                                             </mml:msup>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                     </mml:mfrac>
+                                                    
                                                     <mml:mi>u</mml:mi>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:mo mml:stretchy="false">(</mml:mo>
+                                                        
                                                         <mml:mi>x</mml:mi>
+                                                        
                                                         <mml:mo mml:stretchy="false">)</mml:mo>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">(</mml:mo>
+                                                            
                                                             <mml:mn>1</mml:mn>
+                                                            
                                                             <mml:mo mml:stretchy="false">)</mml:mo>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                         <mml:mo mml:stretchy="false">=</mml:mo>
+                                                        
                                                         <mml:mn>0</mml:mn>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                 </mml:mrow>
+                                                
                                             </mml:mtr>
+                                            
                                             <mml:mtr>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mi>u</mml:mi>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">(</mml:mo>
+                                                            
                                                             <mml:mn>2</mml:mn>
+                                                            
                                                             <mml:mo mml:stretchy="false">)</mml:mo>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                         <mml:mo mml:stretchy="false">=</mml:mo>
+                                                        
                                                         <mml:mn>0</mml:mn>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                 </mml:mrow>
+                                                
                                             </mml:mtr>
+                                            
                                             <mml:mtr>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mfrac>
+                                                        
                                                         <mml:msup>
+                                                            
                                                             <mml:mi>d</mml:mi>
+                                                            
                                                             <mml:mn>2</mml:mn>
+                                                            
                                                         </mml:msup>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mi>d</mml:mi>
+                                                            
                                                             <mml:msup>
+                                                                
                                                                 <mml:mi>x</mml:mi>
+                                                                
                                                                 <mml:mn>2</mml:mn>
+                                                                
                                                             </mml:msup>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                     </mml:mfrac>
+                                                    
                                                     <mml:mi>u</mml:mi>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:mo mml:stretchy="false">(</mml:mo>
+                                                        
                                                         <mml:mi>x</mml:mi>
+                                                        
                                                         <mml:mo mml:stretchy="false">)</mml:mo>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:mrow>
+                                                            
                                                             <mml:mo mml:stretchy="false">(</mml:mo>
+                                                            
                                                             <mml:mn>2</mml:mn>
+                                                            
                                                             <mml:mo mml:stretchy="false">)</mml:mo>
+                                                            
                                                         </mml:mrow>
+                                                        
                                                         <mml:mo mml:stretchy="false">=</mml:mo>
+                                                        
                                                         <mml:mn>0</mml:mn>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                 </mml:mrow>
+                                                
                                             </mml:mtr>
+                                            
                                         </mml:mtable>
+                                        
                                     </mml:mrow>
+                                    
                                     <mml:annotation mml:encoding="StarMath 5.0">left lbrace
+                                        
                                         stack{ u(1)=0# {{d^2} over {d x^2}} u(x)(1)=0# u(2)=0#
+                                        
                                         {{d^2} over {d x^2}} u(x)(2)=0} right
+                                        
                                         none
+                                        
                                     </mml:annotation>
+                                    
                                 </mml:semantics>
+                                
                             </mml:math>
+                            
                         </imagedata>
+                        
                     </imageobject>
+                    
                 </mediaobject>
+                
                 <para>この問題の厳密解は以下のようになることが知られています:</para>
+                
                 <mediaobject>
+                    
                     <imageobject>
+                        
                         <imagedata align="left">
+                            
                             <mml:math>
+                                
                                 <mml:semantics>
+                                    
                                     <mml:mrow>
+                                        
                                         <mml:mi>u</mml:mi>
+                                        
                                         <mml:mrow>
+                                            
                                             <mml:mrow>
+                                                
                                                 <mml:mo mml:stretchy="false">(</mml:mo>
+                                                
                                                 <mml:mi>x</mml:mi>
+                                                
                                                 <mml:mo mml:stretchy="false">)</mml:mo>
+                                                
                                             </mml:mrow>
+                                            
                                             <mml:mo mml:stretchy="false">=</mml:mo>
+                                            
                                             <mml:mfrac>
+                                                
                                                 <mml:mn>1</mml:mn>
+                                                
                                                 <mml:mn>4</mml:mn>
+                                                
                                             </mml:mfrac>
+                                            
                                         </mml:mrow>
+                                        
                                         <mml:mrow>
+                                            
                                             <mml:mo mml:stretchy="false">(</mml:mo>
+                                            
                                             <mml:mrow>
+                                                
                                                 <mml:mn>10</mml:mn>
+                                                
                                                 <mml:mi/>
+                                                
                                                 <mml:mi>log</mml:mi>
+                                                
                                                 <mml:mrow>
+                                                    
                                                     <mml:mrow>
+                                                        
                                                         <mml:mo mml:stretchy="false">(</mml:mo>
+                                                        
                                                         <mml:mn>2</mml:mn>
+                                                        
                                                         <mml:mo mml:stretchy="false">)</mml:mo>
+                                                        
                                                     </mml:mrow>
+                                                    
                                                     <mml:mo mml:stretchy="false">−</mml:mo>
+                                                    
                                                     <mml:mn>3</mml:mn>
+                                                    
                                                 </mml:mrow>
+                                                
                                             </mml:mrow>
+                                            
                                             <mml:mo mml:stretchy="false">)</mml:mo>
+                                            
                                         </mml:mrow>
+                                        
                                         <mml:mi/>
+                                        
                                         <mml:mrow>
+