numerical solutions to differential equations

On Fri, Feb 23, 2007 at 03:32:15PM -0500, richard noel fell wrote:
> Daniel -
> I hope this is sent in plain text as I changed the preferences. 
> Mathematica has a convenient method for returning an interpolating 
> functions for numerical solutions to odes. It is simple and pretty 
> straightforward, even for mma. One can plot so easily with such a 
> functionality.
> 
> Thanks,

My code took two coupled differential equations, and computed an
interpolating polynomial over a finite interval that satisfied certain
boundary conditions.

It used the lagrange interpolation module (interpol.mac), and the
multidimensional Newton's method (mnewton.mac).

However, it was completely specialized to my particular problem. for
example I didn't know the location of the far boundary so that became
one of the parameters in the Newton's method. I used the collocation
spectral method, which worked well, but for simpler systems that
maxima can integrate exactly, Galerkin's method can give you better
accuracy for a given number of terms.

The other option would be to numerically integrate with something like
rk, and then simply interpolate a subset of those data points...

So there are several things that might be done. How does Mathematica's
function work?

Anyone else with suggestions for how I might turn my special purpose
code into a general purpose Galerkin/Collocation spectral method ODE
solver?? 



-- 
Daniel Lakeland
dlakelan at street-artists.org
http://www.street-artists.org/~dlakelan