You are provided a unit square domain where the Laplace operator has a constant

Question

You are provided a unit square domain where the Laplace operator has a constant value of -4 on all internal nodes, but the problem is dx = .000000001, and dy is half of that. Your supervisor has decided that you should solve this problem using a new 4 Gz machine. If you are to do everything with double precision values, how much RAM will you need to compute the solution given the method required? Estimate how long it will take the machine to compute the solution. Are there any other issues that you should point out?

Explanation / Answer

I know this is a strange question to ask but it has got me rather baffled. Ideally, I'm wanting to adapt the code in mathematica so it produces non-combined eigenfunctions for arbitrary domains.

The (very short) code I have been using to get the plots is:

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