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

DOI: 10.1007/BF00370054

- Cite this article as:
- Chrysakis, A.C. & Tsamasphyros, G. Computational Mechanics (1990) 7: 21. doi:10.1007/BF00370054

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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.