J Austral Math Soc Ser B 34 pp401--418, 1993.

A discrete method for the logarithmic-kernel integral equation on an open arc

S. Prössdorf, J. Saranen and I. H. Sloan

Abstract

Here we discuss the stability and convergence of a quadrature method for Symm's integral equation on an open smooth arc. The method is an adaptation of an approach considered by Sloan and Burn for closed curves. Before applying the quadrature scheme, we use a cosine substitution to remove the endpoint singularity of the solution. The family of methods includes schemes with any order 0(h ^p) of convergence.

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Authors

S. Prössdorf

Karl-Weierstrass-Institut für Mathematik, Mohrenstrasse 39, D-O 1086 Berlin, Germany.

J. Saranen

Section of Mathematics, Faculty of Technology, University of Oulu, 90570 Oulu, Finland.

I. H. Sloan

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