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

Denys Dutykh (1, 2, 3, 4)

1 LAMA - Laboratoire de Mathématiques
2 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc
3 UGA [2016-2019] - Université Grenoble Alpes [2016-2019]
4 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques

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.

Mots clés: diffusion; parabolic equations; pseudo-spectral methods; approximation theory

Domaines: Physique [physics]; Mathématiques [math]; Science non linéaire [physics]; Informatique [cs]

Denys Dutykh. A brief introduction to pseudo-spectral methods: application to diffusion problems. Doctoral. Curitiba, Brazil. 2016, pp.55. ⟨cel-01256472v4⟩