FlexPDE is described as 'The Original Unlimited Scripted Multi-Physics Finite Element Solution Environment for Partial Differential Equations is now more powerful than ever!'. There are six alternatives to FlexPDE for a variety of platforms, including Windows, Linux, Mac, Online / Web-based and Chrome OS. The best alternative is SymPy, which is both free and Open Source. Other great apps like FlexPDE are OpenModelica (Free, Open Source), COMSOL Multiphysics (Paid), FEATool Multiphysics (Free Personal) and COSMOSWorks (Paid).
SymPy is a Python library for symbolic computation. The stated goals of the library are to become a full-featured computer algebra system and to keep a simple code base to promote extensibility and comprehensibility.
FEATool Multiphysics is a fully integrated Finite Element FEM CAE simulation toolbox for Matlab. With FEATool you can easily model and simulate heat transfer, fluid flow CFD, structural mechanics, chemical reactions, general PDEs, and more.
StochSD (Stochastic System Dynamics) is a System Dynamics simulation software with focus on stochastics. It is a form of Continuous System Simulation (CSS) that in addition to model and simulate continuous flows between compartments, can handle transitions of discrete entities.