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

Zhongying Chen is a professor of computational mathematics at Sun Yat-Sen University, China. He is the author or co-author of more than 70 professional publications, including the books Generalized Difference Methods for Differential Equations and Approximate Solutions of Operator Equations. He has served on the editorial board of four journals including Advances in Computational Mathematics, and two book series including the Series in Information and Computational Science, China.

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.