Spectral Methods: Algorithms, Analysis and Applications [Paperback]

Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of? basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. A set of basic matlab codes has been made available online to?help the readers to develop their own spectral codes for their specific applications.

Introduction.- Fourier Spectral Methods for Periodic Problems.- Orthogonol Polynomials and Related Approximation Results.- Second-Order Two-Point Boundary Value Problems.- Integral Equations.- High-Order Differential?Equations.- Problems in Unbounded Domains.- Multi-Dimensional Domains.- Mathematical Preliminaries.- Basic iterative methods.- Basic time discretization schemes.- Instructions for routines in Matlab.??

From the reviews:

This is a largely self-contained book on major parts of the application of spectral methods to the numerical solution of partial differential equations & . The material is accessible to & advanced students of mathematics and also to researchers in neighbouring fields wishing to acquire a sound knowledge of methods they might intend to apply. (H. Muthsam, Monatshefte f?r Mathematik, Vol. 170 (2), May, 2013)

This book provides a self-contained presentation for the construction, implementation and analysis of spectral algorithms for some model equations of elliptic, dispersive and parabolic type. & a textbook for graduate students in mathematics and othlóT