Computer algebra system for solving systems of partial differential equations / PDEs

Question

Looking for a symbolic computer algebra system software package, capable of symbolically solving systems of partial differential equations (PDEs). I am certain this can be done with Maple and (possibly) Mathematica. Could you recommend other software packages? They should be able of at least solving systems of linear and quazilinear PDEs containing first-order derivatives of the unknown functions. The coefficients can be constants or functions of the coordinates. I would like to try and see what kind of solutions one gets, when the solution is constant etc.

My preference is working with symbolic PDE solvers, but for the benefit of other readers you can also post about numerical solvers of systems of PDEs, only please make clear whether they are symbolic solvers or numeric ones.

Thanks.

Answer 1

SymPy has some limited support for solving PDEs http://docs.sympy.org/latest/modules/solvers/pde.html

Answer 2

Libmesh Is a finite element library which could be used. Learning curve is on the steep side, but on the plus side its very efficient and runs in parallel and hooks into many other applications.