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Numerical solution of Cauchy type singular integral equations with logarithmic weight, based on arbitrary collocation points

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Abstract

Singular integral equations with a Cauchy type kernel and a logarithmic weight function can be solved numerically by integrating them by a Gauss-type quadrature rule and, further, by reducing the resulting equation to a linear system by applying this equation at an appropriate number of collocation points x k. Until now these x k have been chosen as roots of special functions. In this paper, an appropriate modification of the original method permits the arbitrary choice of x k without any loss in the accuracy. The performance of the method is examined by applying it to a numerical example and a plane crack problem.

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Authors and Affiliations

  1. Section of Mechanics, Department of Engineering Science, The National Technical University of Athens, 5, Heroes of Polytechnion Avenue, GR-15773, Athens, Greece

    A. C. Chrysakis & G. Tsamasphyros

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  1. A. C. Chrysakis
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  2. G. Tsamasphyros
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Communicated by D. E. Beskos, March 8, 1990

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Chrysakis, A.C., Tsamasphyros, G. Numerical solution of Cauchy type singular integral equations with logarithmic weight, based on arbitrary collocation points. Computational Mechanics 7, 21–29 (1990). https://doi.org/10.1007/BF00370054

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  • DOI: https://doi.org/10.1007/BF00370054

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