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Atkinson K.E. The Numerical Solution of Integral Equations of the Second Kind

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Atkinson K.E. The Numerical Solution of Integral Equations of the Second Kind
New York, "Cambridge University Press", 1997, -571p.
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. Practial problems for BIE such as the set up and solution of the discretized 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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