Solving 4-dimensional coupled PDE in matlab?

I have a set of coupled parabolic PDEs I would like to solve in matlab. My problem is that they are in four dimensions, i.e. in time and all three space directions (x, y, z). I know how I can solve such PDEs for one spacial dimension (i.e. following the example here), but not how to do that in three spacial dimensions. Any solutions for that? Or do I have to use other programs?

Edit: According to this link I can solve them, but in my equations I have first and second derivatives in space, which I can not see in the link above (there only are second derivatives in space). Furthermore they are not coupled.

Answer 1

[Alan Weiss]

If you have a Partial Differential Equation Toolbox™ license, then you can most likely solve your problem, assuming that you have a fixed geometry available. You have to put your equations to divergence form first, if you can. Then make sure that your boundary conditions are compatible with the forms the toolbox supports.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation