Is there a numerical ODE solver facility in Maxima / off track -- symbolic ODE solver for series
Subject: Is there a numerical ODE solver facility in Maxima / off track -- symbolic ODE solver for series
From: Richard Fateman
Date: Sat, 04 Apr 2009 16:36:19 -0700
Barton Willis wrote:
> An another way to find Taylor polynomial solutions to DEs is fixed point
> iteration (generally known as Picard iteration for DEs); something like:
>
> (%i89) picard(f,x,y,xo,yo,n) := block([ys],
> ys : taylor(yo,x,xo,n),
> for i : 1 thru n do (
> ys : yo + integrate(subst([y = ys],f),x,xo,x),
> ys : taylor(ys,x,xo,n)),
> ys)$
>
> (%i96) picard(y,x,y,0,1,3);
> (%o96) 1+x+x^2/2+x^3/6+...
>
> (%i97) picard(-y,x,y,0,1,3);
> (%o97) 1-x+x^2/2-x^3/6+...
>
> (%i102) picard(-cos(x*y) - y^2,x,y,0,1,4);
> (%o102) 1-2*x+2*x^2-(5*x^3)/2+(11*x^4)/4+...
>
> Barton
>
>
yes, see also
http://www.cs.berkeley.edu/~fateman/papers/newton.pdf
for picard and newton iteration. Worth pursuing further, I think.