Subject: Change of variable for differential equation
From: Daniel Lakeland
Date: Sun, 17 Jun 2007 15:55:13 -0700
On Sun, Jun 17, 2007 at 06:02:42PM -0400, sen1 at math.msu.edu wrote:
> Without thinking too hard about this, if you really have a
> differential functional equation as in your 'ugly' example, I would
> not try to make such an equation with 't' as an independent variable.
I solved the equations a while back using interpolating polynomials
and the spectral method, but the recent discussion on the numerical
instability of the results of lagrange interpolation polynomials made
me want to go back and reformulate with chebyshev polynomials from the
"orthopoly" package and see if the results were different, indicating
my previous results might be unreliable. The goal then is to map the
chebyshev polynomial on t in [-1,1] to the interval x in [0,xmax] in
my original equations. The equations were nonlinear, hence the attempt
to get maxima to do the heavy lifting.
--
Daniel Lakeland
dlakelan at street-artists.org
http://www.street-artists.org/~dlakelan