Computational Methods for Integral Equations

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CUP Archive, Mar 31, 1988 - Mathematics - 376 pages
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Integral equations form an important class of problems, arising frequently in engineering, and in mathematical and scientific analysis. This textbook provides a readable account of techniques for their numerical solution. The authors devote their attention primarily to efficient techniques using high order approximations, taking particular account of situations where singularities are present. The classes of problems which arise frequently in practice, Fredholm of the first and second kind and eigenvalue problems, are dealt with in depth. Volterra equations, although attractive to treat theoretically, arise less often in practical problems and so have been given less emphasis. Some knowledge of numerical methods and linear algebra is assumed, but the book includes introductory sections on numerical quadrature and function space concepts. This book should serve as a valuable text for final year undergraduate or postgraduate courses, and as an introduction or reference work for practising computational mathematicians, scientists and engineers.
 

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Contents

The space if 2ab
12
Numerical quadrature
24
Introduction to the theory of linear integral equa
66
The Nystrom quadrature method for Fredholm
80
Quadrature methods for Volterra equations of
115
Eigenvalue problems and the Fredholm
152
Expansion methods for Fredholm equations of
167
Analysis of the Galerkin method with orthogonal
212
Numerical performance of algorithms
231
Singular integral equations
261
Integral equations of the first kind
299
Integrodifferential equations
326
Singular expansions
364
References
370
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Numerical Analysis
Raimer Kress
Limited preview - 1998
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