A brief introduction to pseudo-spectral methods: application to diffusion problems
arXiv:1606.05432 · doi:10.1007/978-3-030-31574-0_8
Abstract
The topic of these notes could be easily expanded into a full one-semester course. Nevertheless, we shall try to give some flavour along with theoretical bases of spectral and pseudo-spectral methods. The main focus is made on Fourier-type discretizations, even if some indications on how to handle non-periodic problems via Tchebyshev and Legendre approaches are made as well. The applications presented here are diffusion-type problems in accordance with the topics of the PhD school.
Some minor typos corrected. 55 pages, 40 references, 14 figures. Other author's papers can be downloaded at http://www.denys-dutykh.com/