, Volume 7, Issue 1, pp 21-29

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

Purchase on Springer.com

$39.95 / €34.95 / £29.95*

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

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.

Communicated by D. E. Beskos, March 8, 1990