I'm simulating a biological phenomena with reaction diffusion equations. There are multiple diffusing materials and there are some complex relations about consumption and production of such materials. What is the best way to simulate these interactions? Is finite elements method appropriate? and is there any tool, which solves the PDE (with any method) and give me distribution of chemicals at each time step so that I apply my computations on them?

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    $\begingroup$ Reaction-diffusion equations are parabolic PDEs, and as such they can be solved in a fairly straight-forward way by either finite difference methods or finite element methods. I'm guessing that the reaction terms are nonlinear, so you'll have to account for this appropriately, but we can't say more here unless you give more details about your particular problem. As far as available tools are concerned, there are a number of good general-purpose finite element libraries (deal.II & fenics come to mind) which can handle the problem. You could always just write your own FEM/FDM code too. $\endgroup$ Jun 26 '16 at 15:56
  • $\begingroup$ @TylerOlsen why not make your comment an answer? If you do so, please add that most tools like deal.II or fenics do a spatial discretization and that the time evolution then needs a bit of own coding. $\endgroup$
    – Jan
    Jun 27 '16 at 8:46
  • $\begingroup$ @jan Maybe instead of answering this one question, we can get a larger wiki page going that answers the broader question of "which method/library is good/available for my problem?" It could be something to the effect of: 1) Elliptic : <list of methods, libraries, GUI tools>, 2) Parabolic: <list of methods...> , 3) 1st-order hyperbolic .... etc. Do you know how to get that going? In the meantime, I'll start expanding this comment into a full answer. $\endgroup$ Jun 28 '16 at 11:40
  • $\begingroup$ @TylerOlsen that's a good idea. You may just go ahead and ask such a question and ask the moderators to make it community wiki. I am sure this will have some nice outcomes. $\endgroup$
    – Jan
    Jun 28 '16 at 11:49

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