Add image examples in the differential_equations module 46/10846/1
Sylvestre Ledru [Fri, 15 Mar 2013 12:10:55 +0000 (13:10 +0100)]
Change-Id: I375f56040daed76e2854301c82f9f0c8cee9dda1

16 files changed:
scilab/modules/differential_equations/help/en_US/bvode.xml
scilab/modules/differential_equations/help/en_US/dae.xml
scilab/modules/differential_equations/help/en_US/ode.xml
scilab/modules/differential_equations/help/en_US/odedc.xml
scilab/modules/differential_equations/help/en_US/odeoptions.xml
scilab/modules/helptools/etc/images_md5.txt
scilab/modules/helptools/images/bvode_2.png [new file with mode: 0644]
scilab/modules/helptools/images/bvode_en_US_1.png [new file with mode: 0644]
scilab/modules/helptools/images/bvode_fr_FR_1.png [new file with mode: 0644]
scilab/modules/helptools/images/bvode_pt_BR_1.png [new file with mode: 0644]
scilab/modules/helptools/images/dae_1.png [new file with mode: 0644]
scilab/modules/helptools/images/ode_1.png [new file with mode: 0644]
scilab/modules/helptools/images/odedc_1.png [new file with mode: 0644]
scilab/modules/helptools/images/odedc_2.png [new file with mode: 0644]
scilab/modules/helptools/images/odedc_3.png [new file with mode: 0644]
scilab/modules/helptools/images/odeoptions_1.png [new file with mode: 0644]

index 5bf8b52..264975f 100644 (file)
@@ -1762,17 +1762,22 @@ N=1;// just one differential equation
 m=4;//a fourth order  differential equation
 M=sum(m);
 
-x_low=1;x_up=2; // the x limits
+x_low=1;
+x_up=2; // the x limits
 zeta=[x_low,x_low,x_up,x_up]; //two constraints (on the value of u and its second derivative) on each bound.
 
 //The external functions
 //These functions are called by the solver with zu=[u(x);u'(x);u''(x);u'''(x)]
 
 // - The function which computes the right hand side of the differential equation
-function f=fsub(x,zu),f=(1-6*x^2*zu(4)-6*x*zu(3))/x^3,endfunction
+function f=fsub(x,zu)
+    f=(1-6*x^2*zu(4)-6*x*zu(3))/x^3
+endfunction
 
 // - The function which computes the derivative of fsub with respect to zu
-function df=dfsub(x,zu),df=[0,0,-6/x^2,-6/x],endfunction
+function df=dfsub(x,zu)
+    df=[0,0,-6/x^2,-6/x]
+endfunction
 
 // - The function which computes the ith constraint for a given i
 function g=gsub(i,zu),
@@ -1803,7 +1808,10 @@ function dg=dgsub(i,z)
 endfunction
 
 // - The function which computes the initial guess, unused here
-function [zu,mpar]=guess(x),zu=0;mpar=0,endfunction 
+function [zu,mpar]=guess(x)
+    zu=0;
+    mpar=0;
+endfunction
 
  //define the function which computes the exact value of u for a given x ( for testing purposes)
 function zu=trusol(x)
@@ -1828,15 +1836,18 @@ zu=bvode(xpoints,N,m,x_low,x_up,zeta,ipar,ltol,tol,fixpnt,...
 //check the constraints
 zu([1,3],[1 $]) //should be zero
 plot(xpoints,zu(1,:)) // the evolution of the solution u
-zu1=[];for x=xpoints,zu1=[zu1,trusol(x)]; end;  
+zu1=[];
+for x=xpoints
+    zu1=[zu1,trusol(x)];
+end;
 norm(zu-zu1)
  ]]></programlisting>
             </listitem>
             <listitem>
                 <para>
-                    Same problem using <literal>bvodeS</literal> and an initial guess. 
+                    Same problem using <literal>bvodeS</literal> and an initial guess.
                 </para>
-                <programlisting role="example"><![CDATA[ 
+                <programlisting role="no-scilab-exec"><![CDATA[
 function [z,lhS]=zstart(x)
   z=zeros(5,1);z(5)=1;
   lhS=[0;1];
@@ -2213,12 +2224,48 @@ x=linspace(a,b,N)';
 la0=input('n-th eigenvalue: n= ?');la0=(%pi/2+la0*%pi)^2;
 
 z=bvodeS(x,m,n,a,b,fsub,gsub,zeta,ystart=list(ystart,la0));
+// The same call without any display
+z=bvodeS(x,m,n,a,b,fsub,gsub,zeta,ystart=list(ystart,la0),iprint=1));
+// The same with a lot of display
+z=bvodeS(x,m,n,a,b,fsub,gsub,zeta,ystart=list(ystart,la0),iprint=-1));
 
 clf()
 plot(x,[z(1,:)' z(2,:)']) 
 xtitle(['Startvalue =  '+string(la0);'Eigenvalue = '+string(z(3,1))],'x',' ')
 legend(['y(x)';'y''(x)'])
  ]]></programlisting>
+                <scilab:image localized="true">
+                    function rhs=fsub(x,z)
+                    rhs=[-z(3)*z(1);0]
+                    endfunction
+                    
+                    function g=gsub(i,z)
+                    g=[z(1)-z(2) z(1)-1 z(1)]
+                    g=g(i)
+                    endfunction
+                    
+                    function [z,lhs]=ystart(x,z,la0)
+                    z=[1;0;la0]
+                    lhs=[0;0]
+                    endfunction
+                    
+                    a=0;b=1;
+                    m=[2;1];
+                    n=2;
+                    zeta=[a a b];
+                    N=101;
+                    x=linspace(a,b,N)';
+                    
+                    la0=10;
+                    la0=(%pi/2+la0*%pi)^2;
+                    
+                    z=bvodeS(x,m,n,a,b,fsub,gsub,zeta,ystart=list(ystart,la0),iprint=1);
+                    
+                    plot(x,[z(1,:)' z(2,:)']);
+                    xtitle(['Startvalue =  '+string(la0);'Eigenvalue = '+string(z(3,1))],'x',' ');
+                    legend(['y(x)';'y''(x)']);
+                </scilab:image>
+                
             </listitem>
             <listitem>
                 <para>
@@ -2232,13 +2279,18 @@ legend(['y(x)';'y''(x)'])
 // some preinformation of the solutions y(x) to build the function ystart.
 // z=[y(x);y'(x)]
 
-a=0;b=1;m=2;n=1;
+a=0;
+b=1;
+m=2;
+n=1;
 zeta=[a b];
 N=101;
 tol=1e-8*[1 1];
 x=linspace(a,b,N);
 
-function rhs=fsub(x,z),rhs=-exp(z(1));endfunction
+function rhs=fsub(x,z)
+  rhs=-exp(z(1));
+endfunction
 
 function g=gsub(i,z)
   g=[z(1) z(1)]
@@ -2260,21 +2312,23 @@ for M=[1 4]
    end
 end
 
-// Integrating the ode yield e.g. the two solutions yex and yex1. 
+// Integrating the ode yield e.g. the two solutions yex and yex1.
 
-function y=f(c),y=c.*(1-tanh(sqrt(c)/4).^2)-2;endfunction 
+function y=f(c)
+  y=c.*(1-tanh(sqrt(c)/4).^2)-2;
+endfunction
 c=fsolve(2,f);
 
 function y=yex(x,c)
   y=log(c/2*(1-tanh(sqrt(c)*(1/4-x/2)).^2))
-endfunction 
+endfunction
 
 function y=f1(c1), y=2*c1^2+tanh(1/4/c1)^2-1;endfunction
 c1=fsolve(0.1,f1);
 
 function y=yex1(x,c1)
   y=log((1-tanh((2*x-1)/4/c1).^2)/2/c1/c1)
-endfunction 
+endfunction
 
 disp(norm(z(1,:)-yex(x)),'norm(yex(x)-z(1,:))= ')
 disp(norm(z1(1,:)-yex1(x)),'norm(yex1(x)-z1(1,:))= ')
@@ -2286,6 +2340,68 @@ subplot(2,1,2)
 plot2d(x,z1(1,:),style=[5])
 xtitle(' ','x',' ')
  ]]></programlisting>
+                <scilab:image>
+                    a=0;
+                    b=1;
+                    m=2;
+                    n=1;
+                    zeta=[a b];
+                    N=101;
+                    tol=1e-8*[1 1];
+                    x=linspace(a,b,N);
+                    
+                    function rhs=fsub(x,z)
+                    rhs=-exp(z(1));
+                    endfunction
+                    
+                    function g=gsub(i,z)
+                    g=[z(1) z(1)]
+                    g=g(i)
+                    endfunction
+                    
+                    function [z,lhs]=ystart(x,z,M) 
+                    //z=[4*x*(1-x)*M ; 4*(1-2*x)*M]
+                    z=[M;0]
+                    //lhs=[-exp(4*x*(1-x)*M)]
+                    lhs=0
+                    endfunction
+                    
+                    for M=[1 4]
+                    if M==1
+                    z=bvodeS(x,m,n,a,b,fsub,gsub,zeta,ystart=list(ystart,M),tol=tol);
+                    else
+                    z1=bvodeS(x,m,n,a,b,fsub,gsub,zeta,ystart=list(ystart,M),tol=tol);
+                    end
+                    end
+                    
+                    // Integrating the ode yield e.g. the two solutions yex and yex1.
+                    
+                    function y=f(c)
+                    y=c.*(1-tanh(sqrt(c)/4).^2)-2;
+                    endfunction
+                    c=fsolve(2,f);
+                    
+                    function y=yex(x,c)
+                    y=log(c/2*(1-tanh(sqrt(c)*(1/4-x/2)).^2))
+                    endfunction
+                    
+                    function y=f1(c1), y=2*c1^2+tanh(1/4/c1)^2-1;endfunction
+                    c1=fsolve(0.1,f1);
+                    
+                    function y=yex1(x,c1)
+                    y=log((1-tanh((2*x-1)/4/c1).^2)/2/c1/c1)
+                    endfunction
+                    
+                    disp(norm(z(1,:)-yex(x)),'norm(yex(x)-z(1,:))= ')
+                    disp(norm(z1(1,:)-yex1(x)),'norm(yex1(x)-z1(1,:))= ')
+                    clf();
+                    subplot(2,1,1)
+                    plot2d(x,z(1,:),style=[5])
+                    xtitle('Two different solutions','x',' ')
+                    subplot(2,1,2)
+                    plot2d(x,z1(1,:),style=[5])
+                    xtitle(' ','x',' ')
+                </scilab:image>
             </listitem>
             <listitem>
                 <para>
@@ -2295,7 +2411,7 @@ xtitle(' ','x',' ')
 // DE y'''(x)=1
 // z=[y(x);y'(x);y''(x)]
 // BV: y(-1)=2 y(1)=2
-// Side condition: y(0)=1 
+// Side condition: y(0)=1
 
 a=-1;b=1;c=0;
 // The side condition point c must be included in the array fixpnt.
@@ -2316,7 +2432,7 @@ zeta=[a c b];
 x=linspace(a,b,N);
 
 z=bvodeS(x,m,n,a,b,fsub,gsub,zeta,fixpnt=c);
-          
+
 function y=yex(x)
 y=x.^3/6+x.^2-x./6+1
 endfunction
index fc1141f..1939545 100644 (file)
@@ -475,6 +475,8 @@ y=dae([x0,xd0],0,t,chemres);// returns requested observation time points
 %DAEOPTIONS=list([],1,[],[],[],0,0); // ask  dae mesh points to be returned
 y=dae([x0,xd0],0,4d10,chemres); // without jacobian
 y=dae([x0,xd0],0,4d10,chemres,chemjac); // with jacobian
+ ]]></programlisting>
+        <programlisting role="example"><![CDATA[
 
 //example with C code (C compiler needed) --------------------------------------------------
 //-1- create the C codes in TMPDIR - Vanderpol equation, implicit form
@@ -491,14 +493,18 @@ code=['#include <math.h>'
       ' '
       'void gr22(int *neq, double *t, double *y, int *ng, double *groot, double *rpar, int *ipar)'
       '{ groot[0] = y[0];}']
-cd TMPDIR;      
-mputl(code, 't22.c') 
+cd TMPDIR;
+mputl(code, 't22.c')
 //-2- compile and load them
 ilib_for_link(['res22' 'jac22' 'gr22'],'t22.c',[],'c',TMPDIR+'/Makefile',TMPDIR+'/t22loader.sce');
 exec('t22loader.sce')
 //-3- run
-rtol=[1.d-6;1.d-6];atol=[1.d-6;1.d-4];
-t0=0;y0=[2;0];y0d=[0;-2];t=[20:20:200];ng=1;
+rtol=[1.d-6;1.d-6];
+atol=[1.d-6;1.d-4];
+t0=0;y0=[2;0];
+y0d=[0;-2];
+t=[20:20:200];
+ng=1;
 //simple simulation
 t=0:0.003:300;
 yy=dae([y0,y0d],t0,t,atol,rtol,'res22','jac22');
@@ -509,11 +515,52 @@ plot(yy(1,1),yy(2,1),'r+')
 xstring(yy(1,1)+0.1,yy(2,1),string(nn(1)))
 
 //hot restart for next point
-t01=nn(1);[pp,qq]=size(yy);y01=yy(2:3,qq);y0d1=yy(3:4,qq);
+t01=nn(1);
+[pp,qq]=size(yy);
+y01=yy(2:3,qq);
+y0d1=yy(3:4,qq);
 [yy,nn,hotd]=dae("root",[y01,y0d1],t01,300,atol,rtol,'res22','jac22',ng,'gr22',hotd);
 plot(yy(1,1),yy(2,1),'r+')
 xstring(yy(1,1)+0.1,yy(2,1),string(nn(1)))
  ]]></programlisting>
+        <scilab:image><![CDATA[
+code=['#include <math.h>'
+      'void res22(double *t,double *y,double *yd,double *res,int *ires,double *rpar,int *ipar)'
+      '{res[0] = yd[0] - y[1];'
+      ' res[1] = yd[1] - (100.0*(1.0 - y[0]*y[0])*y[1] - y[0]);}'
+      ' '
+      'void jac22(double *t,double *y,double *yd,double *pd,double *cj,double *rpar,int *ipar)'
+      '{pd[0]=*cj - 0.0;'
+      ' pd[1]=    - (-200.0*y[0]*y[1] - 1.0);'
+      ' pd[2]=    - 1.0;'
+      ' pd[3]=*cj - (100.0*(1.0 - y[0]*y[0]));}'
+      ' '
+      'void gr22(int *neq, double *t, double *y, int *ng, double *groot, double *rpar, int *ipar)'
+      '{ groot[0] = y[0];}']
+cd TMPDIR;
+mputl(code, 't22.c')
+ilib_for_link(['res22' 'jac22' 'gr22'],'t22.c',[],'c',TMPDIR+'/Makefile',TMPDIR+'/t22loader.sce');
+exec('t22loader.sce')
+rtol=[1.d-6;1.d-6];
+atol=[1.d-6;1.d-4];
+t0=0;y0=[2;0];
+y0d=[0;-2];
+t=[20:20:200];
+ng=1;
+t=0:0.003:300;
+yy=dae([y0,y0d],t0,t,atol,rtol,'res22','jac22');
+clf();plot(yy(1,:),yy(2,:))
+[yy,nn,hotd]=dae("root",[y0,y0d],t0,300,atol,rtol,'res22','jac22',ng,'gr22');
+plot(yy(1,1),yy(2,1),'r+')
+xstring(yy(1,1)+0.1,yy(2,1),string(nn(1)))
+t01=nn(1);
+[pp,qq]=size(yy);
+y01=yy(2:3,qq);
+y0d1=yy(3:4,qq);
+[yy,nn,hotd]=dae("root",[y01,y0d1],t01,300,atol,rtol,'res22','jac22',ng,'gr22',hotd);
+plot(yy(1,1),yy(2,1),'r+')
+xstring(yy(1,1)+0.1,yy(2,1),string(nn(1)))
+ ]]></scilab:image>
     </refsection>
     <refsection role="see also">
         <title>See Also</title>
index eabeb21..7f1f612 100644 (file)
@@ -444,6 +444,16 @@ t=0:0.1:%pi;
 y = ode(y0,t0,t,f);
 plot(t,y)
  ]]></programlisting>
+        <scilab:image>
+            function ydot=f(t,y)
+            ydot=y^2-y*sin(t)+cos(t)
+            endfunction
+            y0=0;
+            t0=0;
+            t=0:0.1:%pi;
+            y = ode(y0,t0,t,f);
+            plot(t,y)
+        </scilab:image>
         <para>
             In the following example, we solve the equation <literal>dy/dt=A*y</literal>.
             The exact solution is <literal>y(t)=expm(A*t)*y(0)</literal>, where
index 63d504b..098d4a7 100644 (file)
@@ -145,15 +145,44 @@ yd_k = f (t_k,yc(t_k-),yd(t_(k-1)),1)  (yc is time-continuous: yc(t_k-)=yc(tk))
         <programlisting role="example"><![CDATA[ 
 //Linear system with switching input
 deff('xdu=phis(t,x,u,flag)','if flag==0 then xdu=A*x+B*u; else xdu=1-u;end');
-x0=[1;1];A=[-1,2;-2,-1];B=[1;2];u=0;nu=1;stdel=[1,0];u0=0;t=0:0.05:10;
-xu=odedc([x0;u0],nu,stdel,0,t,phis);x=xu(1:2,:);u=xu(3,:);
+x0=[1;1];
+A=[-1,2;-2,-1];
+B=[1;2];
+u=0;
+nu=1;
+stdel=[1,0];
+u0=0;
+t=0:0.05:10;
+xu=odedc([x0;u0],nu,stdel,0,t,phis);
+x=xu(1:2,:);
+u=xu(3,:);
 nx=2;
 plot2d1('onn',t',x',[1:nx],'161');
 plot2d2('onn',t',u',[nx+1:nx+nu],'000');
-//Fortran external (see fydot2.f): 
+//Fortran external (see fydot2.f):
 norm(xu-odedc([x0;u0],nu,stdel,0,t,'phis'),1)
+ ]]></programlisting>
+        <scilab:image>
+            deff('xdu=phis(t,x,u,flag)','if flag==0 then xdu=A*x+B*u; else xdu=1-u;end');
+            x0=[1;1];
+            A=[-1,2;-2,-1];
+            B=[1;2];
+            u=0;
+            nu=1;
+            stdel=[1,0];
+            u0=0;
+            t=0:0.05:10;
+            xu=odedc([x0;u0],nu,stdel,0,t,phis);
+            x=xu(1:2,:);
+            u=xu(3,:);
+            nx=2;
+            plot2d1('onn',t',x',[1:nx],'161');
+            plot2d2('onn',t',u',[nx+1:nx+nu],'000');
+            //Fortran external (see fydot2.f):
+        </scilab:image>
+        <programlisting role="example"><![CDATA[ 
 
-//Sampled feedback 
+//Sampled feedback
 //
 //        |     xcdot=fc(t,xc,u)
 //  (system)   |
@@ -170,21 +199,79 @@ deff('xcd=f(t,xc,xd,iflag)',...
    'else '
    '  xcd=fd(xd,hc(t,xc));'
    'end']);
-A=[-10,2,3;4,-10,6;7,8,-10];B=[1;1;1];C=[1,1,1];
-Ad=[1/2,1;0,1/20];Bd=[1;1];Cd=[1,1];
+A=[-10,2,3;4,-10,6;7,8,-10];
+B=[1;1;1];
+C=[1,1,1];
+Ad=[1/2,1;0,1/20];
+Bd=[1;1];
+Cd=[1,1];
 deff('st=e(t)','st=sin(3*t)')
 deff('xdot=fc(t,x,u)','xdot=A*x+B*u')
 deff('y=hc(t,x)','y=C*x')
 deff('xp=fd(x,y)','xp=Ad*x + Bd*y')
 deff('u=hd(t,x)','u=Cd*x')
 h=0.1;t0=0;t=0:0.1:2;
-x0c=[0;0;0];x0d=[0;0];nd=2;
+x0c=[0;0;0];
+x0d=[0;0];
+nd=2;
 xcd=odedc([x0c;x0d],nd,h,t0,t,f);
 norm(xcd-odedc([x0c;x0d],nd,h,t0,t,'fcd1')) // Fast calculation (see fydot2.f)
 plot2d([t',t',t'],xcd(1:3,:)');
-xset("window",2);plot2d2("gnn",[t',t'],xcd(4:5,:)');
+xset("window",2);
+plot2d2("gnn",[t',t'],xcd(4:5,:)');
 xset("window",0);
  ]]></programlisting>
+        <scilab:image>
+            deff('xcd=f(t,xc,xd,iflag)',...
+            ['if iflag==0 then '
+            '  xcd=fc(t,xc,e(t)-hd(t,xd));'
+            'else '
+            '  xcd=fd(xd,hc(t,xc));'
+            'end']);
+            A=[-10,2,3;4,-10,6;7,8,-10];
+            B=[1;1;1];
+            C=[1,1,1];
+            Ad=[1/2,1;0,1/20];
+            Bd=[1;1];
+            Cd=[1,1];
+            deff('st=e(t)','st=sin(3*t)')
+            deff('xdot=fc(t,x,u)','xdot=A*x+B*u')
+            deff('y=hc(t,x)','y=C*x')
+            deff('xp=fd(x,y)','xp=Ad*x + Bd*y')
+            deff('u=hd(t,x)','u=Cd*x')
+            h=0.1;t0=0;t=0:0.1:2;
+            x0c=[0;0;0];
+            x0d=[0;0];
+            nd=2;
+            xcd=odedc([x0c;x0d],nd,h,t0,t,f);
+            plot2d([t',t',t'],xcd(1:3,:)');
+        </scilab:image>
+        <scilab:image>
+            deff('xcd=f(t,xc,xd,iflag)',...
+            ['if iflag==0 then '
+            '  xcd=fc(t,xc,e(t)-hd(t,xd));'
+            'else '
+            '  xcd=fd(xd,hc(t,xc));'
+            'end']);
+            A=[-10,2,3;4,-10,6;7,8,-10];
+            B=[1;1;1];
+            C=[1,1,1];
+            Ad=[1/2,1;0,1/20];
+            Bd=[1;1];
+            Cd=[1,1];
+            deff('st=e(t)','st=sin(3*t)')
+            deff('xdot=fc(t,x,u)','xdot=A*x+B*u')
+            deff('y=hc(t,x)','y=C*x')
+            deff('xp=fd(x,y)','xp=Ad*x + Bd*y')
+            deff('u=hd(t,x)','u=Cd*x')
+            h=0.1;t0=0;t=0:0.1:2;
+            x0c=[0;0;0];
+            x0d=[0;0];
+            nd=2;
+            xcd=odedc([x0c;x0d],nd,h,t0,t,f);
+            plot2d2("gnn",[t',t'],xcd(4:5,:)');
+        </scilab:image>
+        
     </refsection>
     <refsection role="see also">
         <title>See Also</title>
index 96ca2f8..a047043 100644 (file)
@@ -141,6 +141,15 @@ y=ode(0,0,%pi,f);
 plot(y(1,:),y(2,:))
 clear %ODEOPTIONS
  ]]></programlisting>
+        <scilab:image>
+            function ydot=f(t,y)
+            ydot=y^2-y*sin(t)+cos(t)
+            endfunction
+            %ODEOPTIONS=[2,0,0,%inf,0,2,500,12,5,0,-1,-1];
+            y=ode(0,0,%pi,f);
+            plot(y(1,:),y(2,:))
+            clear %ODEOPTIONS
+        </scilab:image>
     </refsection>
     <refsection role="see also">
         <title>See Also</title>
index b6c719f..efe78f8 100644 (file)
@@ -550,6 +550,10 @@ bode_ru_RU_1.png=87ec396c51a7cc6aafb148e1aa5f9256
 bode_ru_RU_2.png=95d29219903b7e027aef6a1618855bc0
 bonecolormap_1.png=92247210e578a35b3770d67e94bae718
 buttmag_1.png=9fff0bd432661a67efdde3c0c3a34465
+bvode_2.png=da98ff003070f72b45a30aa94efd4ffd
+bvode_en_US_1.png=f5839719400ab9f8ae4004c3c7bad4ff
+bvode_fr_FR_1.png=f5839719400ab9f8ae4004c3c7bad4ff
+bvode_pt_BR_1.png=f5839719400ab9f8ae4004c3c7bad4ff
 captions_1.png=19ddf03ac04cd2b8ebbed9f218dbaa3e
 cdfbet_1.png=311cb1e4fb872d6f82b2dcafaa5911d1
 cdfbin_1.png=6fd656ebfb423bc5fcf3fdc7e1a82aa8
@@ -590,6 +594,7 @@ cosd_1.png=eb8be1b0523b7acae8c1ef821fdd682f
 csc_1.png=a13e98eda7cbe1284ee48f276b77add7
 csch_1.png=310369792df908182b68dc09625caaca
 cshep2d_1.png=968c99bcf62829dcfe29be5377837624
+dae_1.png=349c58ef4d90dfd500d1020c00802471
 damp_en_US_1.png=e81873a345f84e42ce2c4f4779d3421d
 damp_fr_FR_1.png=e81873a345f84e42ce2c4f4779d3421d
 damp_ja_JP_1.png=e81873a345f84e42ce2c4f4779d3421d
@@ -781,6 +786,11 @@ nyquist_ru_RU_1.png=26826b399f567100ed0118a54c896b5a
 nyquist_ru_RU_2.png=483907f07d0871646b976ed4c6db1ca2
 nyquistfrequencybounds_1.png=cc36d1807604c718839f5e291dc08f5a
 oceancolormap_1.png=bbb2c5edd957782c0a5b7d64761b993
+ode_1.png=bc747e3d4ca0f53146a64200608fc863
+odedc_1.png=57d86d2363e4bb2756f86162c95e1923
+odedc_2.png=e200739457adb87740d6eda59334854b
+odedc_3.png=3d3d5ac8d7a133e26039e93609be5cd0
+odeoptions_1.png=12573ee6be852c456cf883e79dbea5f6
 optim_1.png=a2d9b2e879963549e64862118514b4c8
 optim_sa_1.png=b2a6a1ff9fec247aba2e606e45387997
 orthProj_1.png=dd3a07c86d54c910fc4f253c576f1532
diff --git a/scilab/modules/helptools/images/bvode_2.png b/scilab/modules/helptools/images/bvode_2.png
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