Computational Methods for Integral Equations

This textbook provides a readable account of techniques for numerical solutions.

L. M. Delves (Author), J. L. Mohamed (Author)

9780521357968, Cambridge University Press

Paperback, published 31 March 1988

392 pages
22.9 x 15.2 x 2.2 cm, 0.57 kg

Review of the hardback: 'The material within the book is clear, readable, and well-presented and the task of reading the book proved to be no task at all. Delves and Mohamed's enjoyment of the topic, tempered by their concern for the user's needs, is evident on every page.' Applied Mathematical Modelling

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.

Preface
Introduction
1. The space L2(a,b)
2. Numerical quadrature
3. Introduction to the theory of linear integral equations of the second kind
4. The Nystrom (quadrature) method for Fredholm equations of the second kind
5. Quadrature methods for Volterra equations of the second kind
6. Eigenvalue problems and the Fredholm alternative
7. Expansion methods for Freholm equations of the second kind
8. Numerical techniques for expansion methods
9. Analysis of the Galerkin method with orthogonal basis
10. Numerical performance of algorithms for Fredholm equations of the second kind
11. Singular integral equations
12. Integral equations of the first kind
13. Integro-differential equations
Appendix
References
Index.

Subject Areas: Probability & statistics [PBT]