Integral Equations

1. Front Matter

   Pages i-xiv

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2. Introduction

   • Wolfgang Hackbusch

   Pages 1-24

3. Volterra Integral Equations

   • Wolfgang Hackbusch

   Pages 25-41

4. Theory of Fredholm Integral Equations of the Second Kind

   • Wolfgang Hackbusch

   Pages 42-58

5. Numerical Treatment of Fredholm Integral Equations of the Second Kind

   • Wolfgang Hackbusch

   Pages 59-154

6. Multi-Grid Methods for Solving Systems Arising from Integral Equations of the Second Kind

   • Wolfgang Hackbusch

   Pages 155-200

7. Abel’s Integral Equation

   • Wolfgang Hackbusch

   Pages 201-215

8. Singular Integral Equations

   • Wolfgang Hackbusch

   Pages 216-265

9. The Integral Equation Method

   • Wolfgang Hackbusch

   Pages 266-317

10. The Boundary Element Method

    • Wolfgang Hackbusch

    Pages 318-343

11. Back Matter

    Pages 344-362

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The theory of integral equations has been an active research field for many years and is based on analysis, function theory, and functional analysis. On the other hand, integral equations are of practical interest because of the «boundary integral equation method», which transforms partial differential equations on a domain into integral equations over its boundary. This book grew out of a series of lectures given by the author at the Ruhr-Universitat Bochum and the Christian-Albrecht-Universitat zu Kiel to students of mathematics. The contents of the first six chapters correspond to an intensive lecture course of four hours per week for a semester. Readers of the book require background from analysis and the foundations of numeri­ cal mathematics. Knowledge of functional analysis is helpful, but to begin with some basic facts about Banach and Hilbert spaces are sufficient. The theoretical part of this book is reduced to a minimum; in Chapters 2, 4, and 5 more importance is attached to the numerical treatment of the integral equations than to their theory. Important parts of functional analysis (e. g. , the Riesz-Schauder theory) are presented without proof. We expect the reader either to be already familiar with functional analysis or to become motivated by the practical examples given here to read a book about this topic. We recall that also from a historical point of view, functional analysis was initially stimulated by the investigation of integral equations.

• Approximation
• Integral equation
• Interpolation

• Institut für Informatik und Praktische Mathematik, Christian-Albrechts-Universität Kiel, Kiel, Germany

  Wolfgang Hackbusch

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