The Numerical Solution of Integral Equations of the Second Kind

Erscheinungsjahr 2006
ISBN: 978-0-521-58391-6
Verlag: Cambridge University Press

Buch, Englisch, Band 4, 572 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 1069 g

Reihe: Cambridge Monographs on Applied and Computational Mathematics

This book provides an extensive introduction to the numerical solution of a large class of integral equations. The initial chapters provide a general framework for the numerical analysis of Fredholm integral equations of the second kind, covering degenerate kernel, projection and Nystrom methods. Additional discussions of multivariable integral equations and iteration methods update the reader on the present state of the art in this area. The final chapters focus on the numerical solution of boundary integral equation (BIE) reformulations of Laplace's equation, in both two and three dimensions. Two chapters are devoted to planar BIE problems, which include both existing methods and remaining questions. Practical problems for BIE such as the set up and solution of the discretised BIE are also discussed. Each chapter concludes with a discussion of the literature and a large bibliography serves as an extended resource for students and researchers needing more information on solving particular integral equations.

Autoren/Hrsg.

Atkinson, Kendall E.

Ciarlet, Philippe G.

Iserles, A.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis

Inhaltsverzeichnis

Preface; 1. A brief discussion of integral equations; 2. Degenerate kernel methods; 3. Projection methods; 4. The Nystrom method; 5. Solving multivariable integral equations; 6. Iteration methods; 7. Boundary integral equations on a smooth planar boundary; 8. Boundary integral equations on a piecewise smooth planar boundary; 9. Boundary integral equations in three dimensions; Discussion of the literature; Appendix; Bibliography; Index.