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Multidimensional Weakly Singular Integral Equations

  • Book
  • © 1993

Overview

Authors:
  1. Gennadi Vainikko
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1549)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-XI
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  2. Some problems leading to multidimensional weakly singular integral equations

    • Gennadi Vainikko
    Pages 1-9

  3. Preliminaries

    • Gennadi Vainikko
    Pages 10-23

  4. Smoothness of the solution

    • Gennadi Vainikko
    Pages 24-50

  5. Outlines of the discrete convergence theory

    • Gennadi Vainikko
    Pages 51-59

  6. Piecewise constant collocation and related methods

    • Gennadi Vainikko
    Pages 60-93

  7. Composite cubature algorithms

    • Gennadi Vainikko
    Pages 94-111

  8. Higher order methods

    • Gennadi Vainikko
    Pages 112-136

  9. Nonlinear integral equation

    • Gennadi Vainikko
    Pages 137-144

  10. Back Matter

    Pages 145-159
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Keywords

About this book

The final aim of the book is to construct effective discretization methods to solve multidimensional weakly singular integral equations of the second kind on a region of Rn e.g. equations arising in the radiation transfer theory. To this end, the smoothness of the solution is examined proposing sharp estimates of the growth of the derivatives of the solution near the boundary G. The superconvergence effect of collocation methods at the collocation points is established. This is a book for graduate students and researchers in the fields of analysis, integral equations, mathematical physics and numerical methods. No special knowledge beyond standard undergraduate courses is assumed.

Bibliographic Information

  • Book Title: Multidimensional Weakly Singular Integral Equations

  • Authors: Gennadi Vainikko

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0088979

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1993

  • Softcover ISBN: 978-3-540-56878-0Published: 29 July 1993

  • eBook ISBN: 978-3-540-47773-0Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 168

  • Topics: Analysis, Numerical Analysis

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