Discrete Projection Methods for Integral Equations

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9781853124402: Discrete Projection Methods for Integral Equations

An introductory text at the graduate level on the theory of numerical methods for the solution of integral and boundary integral equations--a topic of great current interest to engineers and applied mathematicians. Provides a comprehensive and unique approach to the numerical analysis of projection methods for integral and boundary integral equations. Although the focus of the book is theoretical, numerical results are presented to illustrate many theoretical developments. The purpose of the book is to provide an introduction to the current mathematical theory used to analyze the convergence and stability of numerical methods for solving a wide variety of integral equations. The authors believe such an analysis is essential to determine the mathematical reliability of a numerical method. Recognition of that reliability is an important component in the choice of a numerical method to solve a particular scientific problem.

The authors analyze discrete projection methods for a variety of integral equations which arise from the reformulation of boundary value problems for partial differential equations. The theory is illustrated by applying it to a wide variety of integral equations: Fredholm, Volterra, Cauchy singular, hyper singular and boundary integral.

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From the Publisher:

It is the first book which gives a comprehensive account of the effect numerical integration errors on projection algorithms for integral and boundary integral equations. It is also the first book to develop the method of fundamental solutions as a discrete projection method. To make the book accessible to as wide an audience as possible, the authors included chapters on functional and numerical analysis which develop all the basic tools necessary to understand subsequent research level results.

Readers will find material here that has not been published before, with both theoretical and computational improvements over previously established results. Special features include new results on numerical integration on emphasis on efficient global methods, many new unpublished convergence results and a chapter devoted to singular and hypersingular integral equations.

Review:

"This book is an extremely friendly introduction and a very useful guide... The authors' intention is to build a bridge between engineers and mathematicians, and in the reviewer's opinion, they have succeeded in doing this.... warmly recommended to anyone engaged in the numerical solution of integral equations and especially to engineers and engineering students.'' --Applied Mechanics Reviews, Vol 50 No 8, August 1997

"this book is highly recommended for serious researchers and student of computational solid and fluid mechanics and should be available in all mathematics and mechanic libraries." --Computational Mechanics Journal, July 1997

this book is an extremely friendly introduction and a very useful guide to hard and big business: the solution of scientific engineering problems by transforming them into integral equations and solving these equations numerically. The publisher may be proud to have such a book in his collection. --Mathematical Reviews, 98c, March 1998 --Mathematical Reviews, 98c, March 1998

"this book is highly recommended for serious researchers and student of computational solid and fluid mechanics and should be available in all mathematics and mechanic libraries." --Computational Mechanics Journal, July 1997

this book is an extremely friendly introduction and a very useful guide to hard and big business: the solution of scientific engineering problems by transforming them into integral equations and solving these equations numerically. The publisher may be proud to have such a book in his collection. --Mathematical Reviews, 98c, March 1998

"this book is highly recommended for serious researchers and student of computational solid and fluid mechanics and should be available in all mathematics and mechanic libraries." --Computational Mechanics Journal, July 1997

this book is an extremely friendly introduction and a very useful guide to hard and big business: the solution of scientific engineering problems by transforming them into integral equations and solving these equations numerically. The publisher may be proud to have such a book in his collection. --Mathematical Reviews, 98c, March 1998

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Published by WIT Press (1996)
ISBN 10: 1853124400 ISBN 13: 9781853124402
New Hardcover Quantity Available: 1
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Book Description WIT Press, 1996. Hardcover. Book Condition: New. book. Bookseller Inventory # M1853124400

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