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

摘要

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 pointsxk. Until now thesexkhave been chosen as roots of special functions. In this paper, an appropriate modification of the original method permits the arbitrary choice ofxkwithout any loss in the accuracy. The performance of the method is examined by applying it to a numerical example and a plane crack problem.