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Presents the state of the art in the study of fast multiscale methods for solving these equations based on wavelets.
List of contents
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.
About the author
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.
Summary
The authors present the state of the art in fast multiscale methods, from traditional numerical methods to the recently developed wavelet-based approach. Theorems of functional analysis used throughout the book are summarised in an appendix. Selected chapters are suitable for a one-semester course for advanced undergraduates or beginning graduates.
