On Rational and Adaptive Spectral Methods

Abstract

In this work, we give a general overview on pseudo-spectral methods. Three types of its variants which are: the adaptive spectral methods conceived for functions with rapid variation in certain domains, the rational adaptive spectral method using rational interpolants, and the adaptive grid Chebyshev points thanks to conformal maps, another type of approximation by the Chebyshev spectral method constituted by a collection of algorithms coded in an objet-oriented MATLAB software environment are considered.