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. Chrysakis
  • G. Tsamasphyros
Article

DOI: 10.1007/BF00370054

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

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 xk. Until now these xk have been chosen as roots of special functions. In this paper, an appropriate modification of the original method permits the arbitrary choice of xk 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.

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • A. C. Chrysakis
    • 1
  • G. Tsamasphyros
    • 1
  1. 1.Section of Mechanics, Department of Engineering ScienceThe National Technical University of AthensAthensGreece