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On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation |
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| Authors: | Rainer Kress Ian H Sloan |
| Institution: | (1) Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Lotzestrasse 16-18, D-37083 Göttingen, Germany;(2) School of Mathematics, University of New South Wales, 2033 Sydney, N.S.W., Australia |
| Abstract: | Summary We describe a quadrature method for the numerical solution of the logarithmic integral equation of the first kind arising from the single-layer approach to the Dirichlet problem for the two-dimensional Helmholtz equation in smooth domains. We develop an error analysis in a Sobolev space setting and prove fast convergence rates for smooth boundary data. |
| Keywords: | 35J05 65N38 65R20 65T05 |
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