Introduction to spectral methods
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.
 Publication:

EAS Publications Series
 Pub Date:
 2006
 DOI:
 10.1051/eas:2006112
 arXiv:
 arXiv:grqc/0609020
 Bibcode:
 2006EAS....21..153G
 Keywords:

 General Relativity and Quantum Cosmology;
 Mathematics  Spectral Theory;
 Physics  Computational Physics
 EPrint:
 20 pages, 15 figures