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I would like to request some literature recommendations covering Chebyshev's pseudospectral collocation method for solving space-time PDEs. It would be nice if it even contained some example problems that cover different types of equations (heat equation, wave equation, etc.), as well as an explanation of how to implement different types of boundary conditions (Dirichlet, Neumann, etc.).

So far I read the book Spectral Methods in MATLAB by Nick Trefethen.

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When I studied spectral collocation methods, I remember that the Chebyshev and Fourier Spectral Methods from Boyd was an easy read (as the Trefethen book you mentioned) with many practical details. If you want a more rigorous exposition, then you can look at the books of Orszag.

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