Learning spectral methods in numerical analysis

Question

I'm trying to learn the theory about spectral methods without any specific ties to a particular program like MATLAB. I tried to search for some lecture videos but it seems very limited and I'm not sure which books are well suited for self-learning about this topic.

Does anyone know of any good books and/or lecture videos for learning about this method?

Answer 1

I would recommend:

• Canuto C. et al. Spectral Methods (springer link).
• Trefethen L. Spectral Methods in Matlab. (This last one guides you through the implementation of the codes in Matlab but it can be easily extended to other programming language).

Hope it helps. Cheers!

Answer 2

Numerical Recipes pages 1083-1096 is a good intro (for me, a non-expert).
They further recommend Boyd. Links: Chebyshev and Fourier Spectral Methods (2013, 688p), PDF under http://www-personal.umich.edu/~jpboyd/