parabolic partial differential equations

My application has some parabolic partial differential equations...which are inter-related and use some variables which the user inputs via a UI from a desktop application.

Can you guide me through as to whi开发者_JAVA百科ch software or library or a particular language would serve the best purpose for the above?

Maybe Python language with:

• PyQt for UI
• SciPy for scientific computing

Or Matlab, or its free counterpart gnu octave or scilab, of freemat.

Or just crank it up in Wolfram Alpha web UI.
http://www.wolframalpha.com/input/?i=X^2%2B2x%2B1%3D0

Or Wolfram Mathematica 8.

Since you said "equations", I'll assume there's more than one and that they're coupled. It's highly unlikely that you'll find a closed-form solution for a problem that difficult.

When I hear "parabolic PDE", the prototype for me is transient diffusion. That usually means a numerical integration forward in time using explicit Euler (small steps, unstable), implicit, or Crank-Nicholson integration scheme.

I'd discretize using finite element methods and weighted residuals. This is how you turn those PDEs into matrix equations.

Once both of those are decided upon, you'll have a set of linear algebra problems to solve repeatedly for each time step. You can use any good linear algebra library you have available in the language of your choice.

Maybe MATLAB or Octave, its open source cousin, could help you here.