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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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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.

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Authors and Affiliations

  1. Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Lotzestrasse 16-18, D-37083, Göttingen, Germany

    Rainer Kress

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

    Ian H. Sloan

Authors
  1. Rainer Kress
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  2. Ian H. Sloan
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Kress, R., Sloan, I.H. On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation. Numer. Math. 66, 199–214 (1993). https://doi.org/10.1007/BF01385694

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  • DOI: https://doi.org/10.1007/BF01385694

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