Description
Springer Spectral Methods Algorithms Analysis And Applications 2013 Edition by Jie Shen Tao Tang Li-Lian Wang
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. Table of contents : 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.