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Implementing Spectral Methods for Partial Differential Equations

Algorithms for Scientists and Engineers

  • Authors
  • David A. Kopriva

Part of the Scientific Computation book series (SCIENTCOMP)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Approximating Functions, Derivatives and Integrals

    1. Front Matter
      Pages 1-1
    2. David A. Kopriva
      Pages 3-38
    3. David A. Kopriva
      Pages 39-57
    4. David A. Kopriva
      Pages 59-87
  3. Approximating Solutions of PDEs

    1. Front Matter
      Pages 89-89
    2. David A. Kopriva
      Pages 91-147
    3. David A. Kopriva
      Pages 149-221
    4. David A. Kopriva
      Pages 247-292
    5. David A. Kopriva
      Pages 293-354
  4. Erratum

    1. David A. Kopriva
      Pages 395-396
  5. Back Matter
    Pages 355-394

About this book

Introduction

This book offers a systematic and self-contained approach to solve partial differential equations numerically using single and multidomain spectral methods. It contains detailed algorithms in pseudocode for the application of spectral approximations to both one and two dimensional PDEs of mathematical physics describing potentials, transport, and wave propagation. David Kopriva, a well-known researcher in the field with extensive practical experience, shows how only a few fundamental algorithms form the building blocks of any spectral code, even for problems with complex geometries. The book addresses computational and applications scientists, as it emphasizes the practical derivation and implementation of spectral methods over abstract mathematics. It is divided into two parts: First comes a primer on spectral approximation and the basic algorithms, including FFT algorithms, Gauss quadrature algorithms, and how to approximate derivatives. The second part shows how to use those algorithms to solve steady and time dependent PDEs in one and two space dimensions. Exercises and questions at the end of each chapter encourage the reader to experiment with the algorithms.

Keywords

Approximation of Derivatives FFT Algorithm Implementation of Spectral Methods Multidomain Spectral Methods Numerical Algorithms PDE PDEs in Realistic Geometries PDEs with Complex Geometries Partial Differential Equations Scientific Computing Solving Complex PDEs Spectral Approximations of PDEs Spectral Method algorithms partial differential equation

Bibliographic information

  • DOI https://doi.org/10.1007/978-90-481-2261-5
  • Copyright Information Springer Science+Business Media B.V. 2009
  • Publisher Name Springer, Dordrecht
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-90-481-2260-8
  • Online ISBN 978-90-481-2261-5
  • Series Print ISSN 1434-8322
  • Buy this book on publisher's site