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A Galerkin-Petrov method 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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A Galerkin-Petrov method for the approximate solution of the complete singular integral equation with Cauchy kernel, based upon the use of two sets of orthogonal polynomials, is considered. The principal result of this paper proves convergence of the approximate solutions to the exact solution making use of a convergence theorem previously given by the author. In conclusion, some related topics such as a first iterate of the approximate solution and a discretized Galerkin-Petrov method are considered. The paper extends to a much more general equation many results obtained by other authors in particular cases.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 25 , Issue 2 , October 1983 , pp. 261 - 275
Copyright
Copyright © Australian Mathematical Society 1983

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