Introduction to spectral methods

Details Introduction to spectral methods Introduction to spectral methods

2006-09-06

arxiv.org/abs/gr-qc/0609020v1

Stellar fluid dynamics and numerical simulations: from the sun to neutron stars, France (2006) 153

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, 15 figures

Scientific paper

10.1051/eas:2006112

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.

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