Hey! I've been trying to tackle this problem but i'm a little lost at the moment and any references or suggestions would be greatly appreciated. Essentially the problem boils down to solving (at least) 3 coupled partial differential equations with (at least) 2 independent variables. Now the solutions and parameters in these equations can be complex-valued and I've had trouble finding any good approaches or packages to help solve these equations. I know a bit of basic complex analysis although haven't taken a formal course in the subject yet, and am just struggling to figure out how I can build an algorithm or use an already known one to solve these complex PDEs. Here is an example of the type of equations I am considering:(adsbygoogle = window.adsbygoogle || []).push({});

## \frac {\partial A}{\partial t} = i (BC - B^*C^*) - \frac{A}{a} ##

## \frac{\partial B}{\partial t} = ibAC - \frac{B}{c} ##

## \frac{\partial C}{\partial x} = idB + e ##

where t and x are the independent variables (real numbers); a,b, c, d and e are parameters (complex); ## i = \sqrt{-1} ##; A, B, and C are the complex-valued states of the system that I am try to solve for. I've checked out a few different PDE solvers such as FiPy but they appear to only work with real values. I have begun looking into methods to solve complex PDEs such as above, but am still looking for methods better suited for my problem so that I have something to work with. If you have any material you'd suggest I look at or know of any packages well-suited to solve such equations, I'd be happy to look in to them.

(I haven't put down any particular prefix for programming language since I don't mind learning something new and better suited for my problem. With that being said, I am most familiar with Python.)

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# Solving complex PDEs

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