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Discrete qualocation methods for logarithmic-kernel integral equations on a piecewise smooth boundary

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Abstract

We consider a fully discrete qualocation method for Symm’s integral equation. The method is that of Sloan and Burn (1992), for which a complete analysis is available in the case of smooth curves. The convergence for smooth curves can be improved by a subtraction of singularity (Jeon and Kimn, 1996). In this paper we extend these results for smooth boundaries to polygonal boundaries. The analysis uses a mesh grading transformation method for Symm’s integral equation, as in Elschner and Graham (1995) and Elschner and Stephan (1996), to overcome the singular behavior of solutions at corners.

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Authors and Affiliations

  1. Department of Mathematics, Ajou University, Suwon, 441-749, Korea

    Y. Jeon

  2. School of Mathematics, University of New South Wales, Sydney, NSW, 2052, Australia

    I.H. Sloan

  3. Institut für Angewandte Mathematik, Universität Hannover, Postfach 6009, D-30060, Hannover, Germany

    E.P. Stephan

  4. Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße, 39, D-10117, Berlin, Germany

    J. Elschner

Authors
  1. Y. Jeon
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  2. I.H. Sloan
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  3. E.P. Stephan
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  4. J. Elschner
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Jeon, Y., Sloan, I., Stephan, E. et al. Discrete qualocation methods for logarithmic-kernel integral equations on a piecewise smooth boundary. Advances in Computational Mathematics 7, 547–571 (1997). https://doi.org/10.1023/A:1018967424040

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  • DOI: https://doi.org/10.1023/A:1018967424040

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