EAS Publications Series

Stellar Fluid Dynamics and Numerical Simulations: From the Sun to Neutron Stars
M. Rieutord and B. Dubrulle (eds)
EAS Publications Series, 21 (2006) 153-180
DOI: 10.1051/eas:2006112

Introduction to spectral methods

P. Grandclément

Laboratoire Univers et ses Théories, Observatoire de Paris, 5 place J. Janssen, 92195 Meudon Cedex, France

Abstract
This proceeding is intended to be a first introduction to spectral methods. It is written around some simple problems that are solved explicitly and in details and that aim at demonstrating the power of those methods. The mathematical foundation of the spectral approximation is first introduced, based on the Gauss quadratures. The two usual basis of Legendre and Chebyshev polynomials are then presented. The next section is devoted to one dimensional equation solvers using only one domain. Three different methods are described. Techniques using several domains are shown in the last section of this paper and their various merits discussed.