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Singularity subtraction in the numerical solution of integral equations

Published online by Cambridge University Press:  17 February 2009

P. M. Anselone
P. M. Anselone
Affiliation:
Oregon State University, Department of Mathematics, Corvallis, Oregon 97331, U.S.A.
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Abstract

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The singularity subtraction technique described by Kantorovich and Krylov in [11] is designed to reduce or overcome the effect of a weakly singular kernel in the numerical solution of integral equations. First, the equation is rearranged in such a way that the singularity of the kernel is at least partially cancelled by the smoothness of the solution, and then numerical integration is applied. We present convergence results and error bounds under general conditions on the nature of the singularity and the numerical integration procedure. Numerical examples demonstrate the benefit of the singularity subtraction technique.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 22 , Issue 4 , April 1981, pp. 408 - 418
Copyright
Copyright © Australian Mathematical Society 1981

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