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Introduction to spectral methods

Published online by Cambridge University Press:  07 June 2006

M. Rieutord ,
B. Dubrulle  and
P. Grandclément
P. Grandclément*
Affiliation:
Laboratoire Univers et ses Théories, Observatoire de Paris, 5 place J. Janssen, 92195 Meudon Cedex, France
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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.

Type
Research Article
Information
European Astronomical Society Publications Series , Volume 21: Stellar Fluid Dynamics and Numerical Simulations: From the Sun to Neutron Stars , 2006 , pp. 153 - 180
Copyright
© EAS, EDP Sciences, 2006

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