rtaylor - obtain the Taylor series for an ODE or PDE system
rtaylor( solved , options )
rtaylor( solved , vars , options )
Parameters
solved - system in solved form
vars - (optional) solving variables of the system
options - (optional) sequence of options to specify the ranking for the solved form, initial data, and the order of the Taylor series
> with(Rif):
A simple ODE
> rtaylor([diff(f(x),x,x)=-f(x)],order=4);
A PDE system with a single dependent variable
>
rtaylor([diff(f(x,y),y,y)=diff(f(x,y),x)*f(x,y),
diff(f(x,y),x,x)=2*f(x,y)], order=3);
A PDE system with two dependent variables
>
rtaylor([diff(f(x,y),x,x)=diff(g(x,y),y),
diff(f(x,y),y,y)=diff(g(x,y),x),
diff(g(x,y),x)=diff(g(x,y),y)]);
An example using initial data
> sys := {diff(f(x,y),x,x)=0,diff(f(x,y),x,y)=0};
> id := initialdata(sys);
> rtaylor(sys, id, order=3);
An example using specified initial data and an expansion point
> ids := eval(eval(id),{_F1(y)=sin(y),_C1=1});
> rtaylor(sys, ids, order=3, point=[x=1,y=Pi]);
caseplot , rifsimp , rifsimp[nonlinear]