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I try to numerically solve the following partial differential equation for N(r,z) with a Dirichlet boundary condition.

[tex]-\frac{\partial^2N}{\partial r^2}-\frac{\partial^2N}{\partial z^2} + f(r,z) \frac{\partial N}{\partial r} + g(r,z) \frac{\partial N}{\partial z} = h(r,z)[/tex]

Mathematica is apparently not able to do it, because it is not an initial value problem. I also wasn't successful with the matlab pde tool. The Crank-Nicolson approximation seems to be the right way to go.

My question is which is the best software for solving this problem, so that I don't have to implement the algorithm myself.

Thanks a lot :)