The Numerical Solution of Integral Equations of the Second Kind (Cambridge Monographs on Applied and Computational Mathematics)
Cambridge University Press, 9/18/1997
EAN 9780521583916, ISBN10: 0521583918
Hardcover, 572 pages, 23.5 x 16 x 4.1 cm
Language: English
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.
Preface
1. A brief discussion of integral equations
2. Degenerate kernel methods
3. Projection methods
4. The Nystrom method
5. Solving multivariable integral equations
6. Iteration methods
7. Boundary integral equations on a smooth planar boundary
8. Boundary integral equations on a piecewise smooth planar boundary
9. Boundary integral equations in three dimensions
Discussion of the literature
Appendix
Bibliography
Index.
' This outstanding monograph ... represents a major milestone in the list of books on the numerical solution of integral equations ... deserves to be on the shelf of any researcher and graduate student interested in the numerical solution of elliptic boundary-value problems.' H. Brunner, Mathematics Abstracts 'It will become the standard reference in the area.' Zietschrift fur Angwandte Mathematik und Physik