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A convergence theorem for singular integral equations

Published online by Cambridge University Press:  17 February 2009

David Elliott
David Elliott
Affiliation:
Mathematics Department, University of Tasmania, Box 252C, G.P.O., Hobart, Tasmania, 7001
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Abstract

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The principal result of this paper states sufficient conditions for the convergence of the solutions of certain linear algebraic equations to the solution of a (linear) singular integral equation with Cauchy kernel. The motivation for this study has been the need to provide a convergence theory for a collocation method applied to the singular integral equation taken over the arc (−1, 1). However, much of the analysis will be applicable both to other approximation methods and to singular integral equations taken over other arcs or contours. An estimate for the rate of convergence is also given.

Type
Research Article
Information
The ANZIAM Journal , Volume 22 , Issue 4 , April 1981 , pp. 539 - 552
Copyright
Copyright © Australian Mathematical Society 1981

References

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