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Periodic Integral and Pseudodifferential Equations with Numerical Approximation

  • Jukka Saranen
  • Gennadi Vainikko

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Jukka Saranen, Gennadi Vainikko
    Pages 1-34
  3. Jukka Saranen, Gennadi Vainikko
    Pages 35-70
  4. Jukka Saranen, Gennadi Vainikko
    Pages 71-103
  5. Jukka Saranen, Gennadi Vainikko
    Pages 105-132
  6. Jukka Saranen, Gennadi Vainikko
    Pages 133-165
  7. Jukka Saranen, Gennadi Vainikko
    Pages 167-198
  8. Jukka Saranen, Gennadi Vainikko
    Pages 199-238
  9. Jukka Saranen, Gennadi Vainikko
    Pages 239-254
  10. Jukka Saranen, Gennadi Vainikko
    Pages 255-291
  11. Jukka Saranen, Gennadi Vainikko
    Pages 293-324
  12. Jukka Saranen, Gennadi Vainikko
    Pages 325-354
  13. Jukka Saranen, Gennadi Vainikko
    Pages 355-400
  14. Jukka Saranen, Gennadi Vainikko
    Pages 401-440
  15. Back Matter
    Pages 441-452

About this book

Introduction

Classical boundary integral equations arising from the potential theory and acoustics (Laplace and Helmholtz equations) are derived. Using the parametrization of the boundary these equations take a form of periodic pseudodifferential equations. A general theory of periodic pseudodifferential equations and methods of solving are developed, including trigonometric Galerkin and collocation methods, their fully discrete versions with fast solvers, quadrature and spline based methods. The theory of periodic pseudodifferential operators is presented in details, with preliminaries (Fredholm operators, periodic distributions, periodic Sobolev spaces) and full proofs. This self-contained monograph can be used as a textbook by graduate/postgraduate students. It also contains a lot of carefully chosen exercises.

Keywords

Boundary value problem Helmholtz equation Periodic pseudodifferential equations Sobolev space boundary integral equations fast solvers fully discrete methods numerical analysis periodic integral equations

Authors and affiliations

  • Jukka Saranen
    • 1
  • Gennadi Vainikko
    • 2
  1. 1.Department of Mathematical SciencesUniversity of OuluOuluFinland
  2. 2.Institute of MathematicsHelsinki University of TechnologyEspooFinland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-04796-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-07538-4
  • Online ISBN 978-3-662-04796-5
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site
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