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Periodic Integral and Pseudodifferential Equations with Numerical Approximation

  • Book
  • © 2002

Overview

Authors:
  1. Jukka Saranen

    1. Department of Mathematical Sciences, University of Oulu, Oulu, Finland

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    You can also search for this author in PubMed   Google Scholar

  2. Gennadi Vainikko

    1. Institute of Mathematics, Helsinki University of Technology, Espoo, Finland

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    You can also search for this author in PubMed   Google Scholar

  • An attractive book in the intersection of analysis and numerical analysis
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Preliminaries

    • Jukka Saranen, Gennadi Vainikko
    Pages 1-34

  3. Single Layer and Double Layer Potentials

    • Jukka Saranen, Gennadi Vainikko
    Pages 35-70

  4. Solution of Boundary Value Problems by Integral Equations

    • Jukka Saranen, Gennadi Vainikko
    Pages 71-103

  5. Singular Integral Equations

    • Jukka Saranen, Gennadi Vainikko
    Pages 105-132

  6. Boundary Integral Operators in Periodic Sobolev Spaces

    • Jukka Saranen, Gennadi Vainikko
    Pages 133-165

  7. Periodic Integral Equations

    • Jukka Saranen, Gennadi Vainikko
    Pages 167-198

  8. Periodic Pseudodifferential Operators

    • Jukka Saranen, Gennadi Vainikko
    Pages 199-238

  9. Trigonometric Interpolation

    • Jukka Saranen, Gennadi Vainikko
    Pages 239-254

  10. Galerkin Method and Fast Solvers

    • Jukka Saranen, Gennadi Vainikko
    Pages 255-291

  11. Trigonometric Collocation

    • Jukka Saranen, Gennadi Vainikko
    Pages 293-324

  12. Integral Equations on an Open Arc

    • Jukka Saranen, Gennadi Vainikko
    Pages 325-354

  13. Quadrature Methods

    • Jukka Saranen, Gennadi Vainikko
    Pages 355-400

  14. Spline Approximation Methods

    • Jukka Saranen, Gennadi Vainikko
    Pages 401-440

  15. Back Matter

    Pages 441-452
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematical Sciences, University of Oulu, Oulu, Finland

    Jukka Saranen

  • Institute of Mathematics, Helsinki University of Technology, Espoo, Finland

    Gennadi Vainikko

Bibliographic Information

  • Book Title: Periodic Integral and Pseudodifferential Equations with Numerical Approximation

  • Authors: Jukka Saranen, Gennadi Vainikko

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-662-04796-5

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2002

  • Hardcover ISBN: 978-3-540-41878-8Published: 06 November 2001

  • Softcover ISBN: 978-3-642-07538-4Published: 08 December 2010

  • eBook ISBN: 978-3-662-04796-5Published: 09 March 2013

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XI, 452

  • Topics: Analysis, Computational Mathematics and Numerical Analysis

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