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Collocation with Chebyshev polynomials for Symm's integral equation on an interval

Published online by Cambridge University Press:  17 February 2009

I. H. Sloan  and
E. P. Stephan
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Abstract

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A collocation method for Symm's integral equation on an interval (a first-kind integral equation with logarithmic kernel), in which the basis functions are Chebyshev polynomials multiplied by an appropriate singular function and the collocation points are Chebyshev points, is analysed. The novel feature lies in the analysis, which introduces Sobolev norms that respect the singularity structure of the exact solution at the ends of the interval. The rate of convergence is shown to be faster than any negative power of n, the degree of the polynomial space, if the driving term is smooth.

Type
Research Article
Information
The ANZIAM Journal , Volume 34 , Issue 2 , October 1992 , pp. 199 - 211
Copyright
Copyright © Australian Mathematical Society 1992

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