Integral Equations: Theory and Numerical Treatment

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This volume explores integral equations, devoting special chapters to Abel’s integral equations and the singular integral equation with the Cauchy kernel. Other chapters focus on the integral equation method and the boundary element method. While a small section affords some theoretical grounding in integral equations (covering such topics as existence and regularity), the larger part of the book is devoted to a description and analysis of the discretization methods (such as Galerkin, collocation and Nystrom). Also, the multi-grid method for the solution of discrete equations is analyzed. The most prominent application of integral equations occurs in the use of the boundary element method, which 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. The book is intended for students of mathematics, as well as postgraduates.