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: Barton Willis
Date: Sat, 4 Apr 2009 17:00:28 -0500
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