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I am interested in working with systems of PDEs in two spatial dimensions, as part of a mathematical modeling project. The systems of PDEs are coupled, and there is no convenient reduction to 1 spatial dimension (due to the particular constraints of the modeling problem). It is my understanding that the built-in MATLAB solvers for PDEs are for problems in 1 spatial dimension.

Can anyone suggest a package for MATLAB that can solve coupled PDEs numerically in multiple spatial dimensions?

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  • $\begingroup$ You're likely thinking of COMSOL Multiphysics. $\endgroup$ – Brian Borchers Aug 25 '16 at 16:07
  • $\begingroup$ MATLAB PDE Toolbox solves PDE of this type but since it is a Mathworks product, it isn't "third-party." $\endgroup$ – Bill Greene Aug 25 '16 at 16:23
  • $\begingroup$ @Snakelet Yes, that is better. By the way, the MATLAB PDE Toolbox is not restricted to one space dimension, and in the current version (2016a) can even handle three dimensions (it's been stuck at two basically since COMSOL -- which started as the PDE toolbox -- moved out). $\endgroup$ – Christian Clason Aug 25 '16 at 17:16
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The built-in pdepe function is indeed limited to 1D elliptic and parabolic equations. The Mathworks also offers the PDE toolbox for 2D and 3D problems. Alternatively, the external FEATool Multiphysics MATLAB toolbox supports systems of coupled PDEs in any dimension.

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