Spectral Methods

Algorithms, Analysis and Applications

  • Jie Shen
  • Tao Tang
  • Li-Lian Wang
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 41)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Jie Shen, Tao Tang, Li-Lian Wang
    Pages 1-22
  3. Jie Shen, Tao Tang, Li-Lian Wang
    Pages 23-46
  4. Jie Shen, Tao Tang, Li-Lian Wang
    Pages 47-140
  5. Jie Shen, Tao Tang, Li-Lian Wang
    Pages 141-180
  6. Jie Shen, Tao Tang, Li-Lian Wang
    Pages 181-200
  7. Jie Shen, Tao Tang, Li-Lian Wang
    Pages 201-236
  8. Jie Shen, Tao Tang, Li-Lian Wang
    Pages 237-298
  9. Jie Shen, Tao Tang, Li-Lian Wang
    Pages 299-366
  10. Jie Shen, Tao Tang, Li-Lian Wang
    Pages 367-413
  11. Back Matter
    Pages 415-470

About this book

Introduction

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.

Keywords

numerical analysis orthogonal polynomials/functions scientific computing spectral methods

Authors and affiliations

  • Jie Shen
    • 1
  • Tao Tang
    • 2
  • Li-Lian Wang
    • 3
  1. 1.Dept. MathematicsPurdue UniversityWest LafayetteUSA
  2. 2.Dept. MathematicsHong Kong Baptist UniversityKowloonHong Kong/PR China
  3. 3.School of Physical & Mathematical Sci.Nanyang Technological UniversitySingaporeSingapore

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-71041-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-71040-0
  • Online ISBN 978-3-540-71041-7
  • Series Print ISSN 0179-3632
  • About this book