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International Journal of Mathematics and Mathematical Sciences
Volume 28, Issue 3, Pages 127-179
http://dx.doi.org/10.1155/S0161171201010924

Numerical methods of computation of singular and hypersingular integrals

Penza State University, Krasnay Street, 40, Penza 440017, Russia

Received 21 September 2000; Revised 5 August 2001

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In solving numerous problems in mathematics, mechanics, physics, and technology one is faced with necessity of calculating different singular integrals. In analytical form calculation of singular integrals is possible only in unusual cases. Therefore approximate methods of singular integrals calculation are an active developing direction of computing in mathematics. This review is devoted to the optimal with respect to accuracy algorithms of the calculation of singular integrals with fixed singularity, Cauchy and Hilbert kernels, polysingular and many-dimensional singular integrals. The isolated section is devoted to the optimal with respect to accuracy algorithms of the calculation of the hypersingular integrals.