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.



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  • $\begingroup$ I am looking for solving symbolically $\endgroup$ – Jay Jun 14 '15 at 19:29
  • $\begingroup$ I guess it's okay if people post about numerical solvers... this subject seems to be less popular and any input helps :) $\endgroup$ – Jay Jun 14 '15 at 20:33
  • $\begingroup$ Numerical PDE solvers are a dime a dozen, and the one you should use depends very much on the PDE. Symbolic solvers are much rarer. You should clarify what kind of PDEs you have and what kind of solutions you are looking for. $\endgroup$ – asmeurer Jun 15 '15 at 6:58
  • $\begingroup$ Edited. I would like to try solving systems of linear / quazilinear PDEs and see what kind of solutions does one get. I have never heard of a free software package with this capability, but I could be missing something useful. $\endgroup$ – Jay Jun 15 '15 at 15:42

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

  • $\begingroup$ For what I understand, SimPy can solve single PDEs only,... would be able to solve a system of PDEs $\endgroup$ – Jay Jun 14 '15 at 17:18

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.


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