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

Published online by Cambridge University Press:  17 February 2009

S. Prössdorf ,
J. Saranen  and
I. H. Sloan
S. Prössdorf
Affiliation:
Karl-Weierstrass-Institut für Mathematik, Mohrenstrasse 39, D-O 1086 Berlin, Germany.
J. Saranen
Affiliation:
Section of Mathematics, Faculty of Technology, University of Oulu, 90570 Oulu, Finland.
I. H. Sloan
Affiliation:
School of Mathematics, University of New South Wales, Sydney, N.S.W. 2033, Australia.
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Abstract

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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 O(hp) of convergence.

Type
Research Article
Information
The ANZIAM Journal , Volume 34 , Issue 4 , April 1993 , pp. 401 - 418
Copyright
Copyright © Australian Mathematical Society 1993

References

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