J Austral Math Soc Ser B 34 pp199--211, 1992.

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

I. H. Sloan and E. P. Stephan

Abstract

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.

Browse the article

Authors

I. H. Sloan

School of Mathematics, University of New South Wales, Sydney, N.S.W. 2033, Australia.

E. P. Stephan

School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA.

Present address: Institut für Angewandte Mathématik, Universität Hannover, Hannover 1, Germany.