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  3. The Numerical Solution of Integral Equations of the Second Kind
  • Cited by 806
Publisher:
Cambridge University Press
Online publication date:
March 2010
Print publication year:
1997
Online ISBN:
9780511626340
DOI:
https://doi.org/10.1017/CBO9780511626340
Subjects:
Mathematics, Computational Science, Numerical Analysis and Computational Science
Series:
Cambridge Monographs on Applied and Computational Mathematics (4)
Information

Book description

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.

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