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The topic of these notes could be easily expanded into a full one-semestercourse. Nevertheless, we shall try to give some flavour along with theoreticalbases of spectral and pseudo-spectral methods. The main focus is made onFourier-type discretizations, even if some indications on how to handlenon-periodic problems via Tchebyshev and Legendre approaches are made as well.The applications presented here are diffusion-type problems in accordance withthe topics of the PhD school.

A brief introduction to pseudo-spectral methods: application to diffusion problems