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Synopsis
Volterra and Fredholm integral equations form the domain of this book. Special chapters are devoted to Abel's integral equations and the singular integral equation with the Cauchy kernel; others focus on the integral equation method and the boundary element method (BEM). While a small section affords some theoretical grounding in integral equations (covering existence, regularity, etc.), the larger part of the book is devoted to a description and analysis of the discretisation methods (Galerkin / collocation / Nyström). Also the multigrid method for the solution of discrete equations is analysed. The most prominent application of integral equations occurs in the use of the boundary element method, which here is discussed from the numerical point of view in particular. New results about numerical integration and the panel clustering technique are included. Many chapters have an introductory character, while special subsections give more advanced information. Intended readers are students of mathematics as well as postgraduates.
Booknews
Growing out of a series of lectures given by the author at the Ruhr- Universitat Bochum and the Christian-Albrecht-Universitat zu Kiel, this volume begins with basics from analysis, functional analysis, and numerical mathematics, followed by a consideration of Volterra integral equations. After these, Fredholm integral equations of the second kind are investigated theoretically and then numerically. Special chapters are devoted to Abel's integral equations and the singular integral equation with Cauchy kernel; others focus on the integral equation method and the boundary element method. A revised translation of the 1989 German original. Annotation c. Book News, Inc., Portland, OR (booknews.com)