Multiscale Methods for Fredholm Integral Equations

Presents the state of the art in the study of fast multiscale methods for solving these equations based on wavelets.

Zhongying Chen (Author), Charles A. Micchelli (Author), Yuesheng Xu (Author)

9781107103474, Cambridge University Press

Hardback, published 16 July 2015

552 pages, 25 b/w illus. 25 tables
23.7 x 16 x 4 cm, 0.97 kg

The recent appearance of wavelets as a new computational tool in applied mathematics has given a new impetus to the field of numerical analysis of Fredholm integral equations. This book gives an account of the state of the art in the study of fast multiscale methods for solving these equations based on wavelets. The authors begin by introducing essential concepts and describing conventional numerical methods. They then develop fast algorithms and apply these to solving linear, nonlinear Fredholm integral equations of the second kind, ill-posed integral equations of the first kind and eigen-problems of compact integral operators. Theorems of functional analysis used throughout the book are summarised in the appendix. The book is an essential reference for practitioners wishing to use the new techniques. It may also be used as a text, with the first five chapters forming the basis of a one-semester course for advanced undergraduates or beginning graduates.

Preface
Introduction
1. A review on the Fredholm approach
2. Fredholm equations and projection theory
3. Conventional numerical methods
4. Multiscale basis functions
5. Multiscale Galerkin methods
6. Multiscale Petrov–Galerkin methods
7. Multiscale collocation methods
8. Numerical integrations and error control
9. Fast solvers for discrete systems
10. Multiscale methods for nonlinear integral equations
11. Multiscale methods for ill-posed integral equations
12. Eigen-problems of weakly singular integral operators
Appendix. Basic results from functional analysis
References
Symbols
Index.

Subject Areas: Numerical analysis [PBKS], Calculus & mathematical analysis [PBK], Mathematics [PB]