Spectral methods: algorithms, analysis and applications

by Shen, Jie

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Title Statements

Full title :Spectral methods : algorithms, analysis and applications / Jie Shen, Tao Tang, Li-Lian Wang.

Summary

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.

Edition Statements

Publication Date:©2011.

Publication Statements

Publisher(s):Springer
Place of Publication:Berlin
Language:eng
Publication Date:©2011.

The Physical Object

Description:1 online resource (xvi, 470 pages)

Edition Identifiers

ISBN:9783540710417, 3540710418, 9783540710400, 354071040X
DOI:10.1007/978-3-540-71041-7.
oclc:ocn755926654
LC Classification:QA320
Dewey Decimal:515/.7222

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.¡¡.