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I'm finishing up a term project in a numerical analysis course, and one of the last things left that I need to do is provide a brief survey of the methods used by modern researchers to solve the 2-D wave equation initial boundary value problem. My group solved this equation for an octagonal boundary using a basic numerical discretization method, converting it into a system of ordinary differential equations in time and then solving this system by several numerical methods for ODE's.

I'm looking for some info on methods used in the real world by modern researchers, and I haven't had much luck so far. Obviously there's the separation of variables method, but that's rarely used except when the problem has a convenient symmetry. I'm also aware of the Green's function method, which I presume is easy to implement by converting the problem into one of numerical integration. So my question is whether anyone can point me towards some resources that would explain what's being done these days for the 2-D wave equation IBVP. I don't need to go into too much depth or detail as I'm only asked to do a brief survey of the literature and to present it at an undergraduate level.

Any help would be greatly appreciated!

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# Advanced Numerical Methods for Wave Eqn?

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