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  • © 1993

Multidimensional Weakly Singular Integral Equations

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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
  2. Preliminaries

    • Gennadi Vainikko
    Pages 10-23
  3. Smoothness of the solution

    • Gennadi Vainikko
    Pages 24-50
  4. Outlines of the discrete convergence theory

    • Gennadi Vainikko
    Pages 51-59
  5. Composite cubature algorithms

    • Gennadi Vainikko
    Pages 94-111
  6. Higher order methods

    • Gennadi Vainikko
    Pages 112-136
  7. Nonlinear integral equation

    • Gennadi Vainikko
    Pages 137-144
  8. Back Matter

    Pages 145-159

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.

Keywords

  • Derivative
  • Integral Equations
  • Integral equation
  • Numerical Solution
  • Smooth function
  • cubature
  • numerical methods

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

Buying options

eBook USD 29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions