Article

Computational Mechanics

, Volume 7, Issue 1, pp 21-29

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

  • A. C. ChrysakisAffiliated withSection of Mechanics, Department of Engineering Science, The National Technical University of Athens
  • , G. TsamasphyrosAffiliated withSection of Mechanics, Department of Engineering Science, The National Technical University of Athens

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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.