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Computational Methods for Linear Integral Equations

  • Book
  • © 2002

Overview

Authors:
  1. Prem K. Kythe

    1. University of New Orleans, New Orleans, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Pratap Puri

    1. Department of Mathematics, University of New Orleans, New Orleans, USA

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    You can also search for this author in PubMed   Google Scholar

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Introduction

    • Prem K. Kythe, Pratap Puri
    Pages 1-43

  3. Eigenvalue Problems

    • Prem K. Kythe, Pratap Puri
    Pages 44-89

  4. Equations of the Second Kind

    • Prem K. Kythe, Pratap Puri
    Pages 90-105

  5. Classical Methods for FK2

    • Prem K. Kythe, Pratap Puri
    Pages 106-129

  6. Variational Methods

    • Prem K. Kythe, Pratap Puri
    Pages 130-145

  7. Iteration Methods

    • Prem K. Kythe, Pratap Puri
    Pages 146-174

  8. Singular Equations

    • Prem K. Kythe, Pratap Puri
    Pages 175-212

  9. Weakly Singular Equations

    • Prem K. Kythe, Pratap Puri
    Pages 213-251

  10. Cauchy Singular Equations

    • Prem K. Kythe, Pratap Puri
    Pages 252-285

  11. Sinc-Galerkin Methods

    • Prem K. Kythe, Pratap Puri
    Pages 286-320

  12. Equations of the First Kind

    • Prem K. Kythe, Pratap Puri
    Pages 321-374

  13. Inversion of Laplace Transforms

    • Prem K. Kythe, Pratap Puri
    Pages 375-415

  14. Back Matter

    Pages 416-508
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Keywords

About this book

This book presents numerical methods and computational aspects for linear integral equations. Such equations occur in various areas of applied mathematics, physics, and engineering. The material covered in this book, though not exhaustive, offers useful techniques for solving a variety of problems. Historical information cover­ ing the nineteenth and twentieth centuries is available in fragments in Kantorovich and Krylov (1958), Anselone (1964), Mikhlin (1967), Lonseth (1977), Atkinson (1976), Baker (1978), Kondo (1991), and Brunner (1997). Integral equations are encountered in a variety of applications in many fields including continuum mechanics, potential theory, geophysics, electricity and mag­ netism, kinetic theory of gases, hereditary phenomena in physics and biology, renewal theory, quantum mechanics, radiation, optimization, optimal control sys­ tems, communication theory, mathematical economics, population genetics, queue­ ing theory, and medicine. Most of the boundary value problems involving differ­ ential equations can be converted into problems in integral equations, but there are certain problems which can be formulated only in terms of integral equations. A computational approach to the solution of integral equations is, therefore, an essential branch of scientific inquiry.

Reviews

"The monograph is devoted to numerical methods for solving one-dimensional linear integral equations. Fredholm and Volterra integral equations of first and second kinds are considered. The authors pay more attention to computational aspects of solving integral equations. A lot of numerical examples and results of computations by computers are presented."   —Mathematical Reviews

"This book presents numerical methods and computational aspects for linear integral equations that appear in various areas of applied mathematics, physics, and engineering…. The book is an excellent reference for graduate students and researchers in mathematics and engineering."   —Memoriile Sectiilor Stiintifice

Authors and Affiliations

  • University of New Orleans, New Orleans, USA

    Prem K. Kythe

  • Department of Mathematics, University of New Orleans, New Orleans, USA

    Pratap Puri

Bibliographic Information

  • Book Title: Computational Methods for Linear Integral Equations

  • Authors: Prem K. Kythe, Pratap Puri

  • DOI: https://doi.org/10.1007/978-1-4612-0101-4

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 2002

  • Hardcover ISBN: 978-0-8176-4192-4Published: 26 April 2002

  • Softcover ISBN: 978-1-4612-6612-9Published: 23 October 2012

  • eBook ISBN: 978-1-4612-0101-4Published: 28 June 2011

  • Edition Number: 1

  • Number of Pages: XVIII, 508

  • Topics: Integral Equations, Numeric Computing, Several Complex Variables and Analytic Spaces

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