On the application of numerical integration rules to the solution of some singular integral equations

Abstract

Abstract The numerical solution of one- or two-dimensional singular integral equations with singularities in their kernels can be achieved in several cases by reducing such an equation to a system of linear equations through use of appropriate numerical integration rules and collocation points. These points are selected in such a way that a numerical integration rule for regular integrals applies also to singular integrals. This method has been already widely applied to the case of one-dimensional Cauchy-type singular integral equations. In this paper analogous techniques are described for the cases of one-dimensional singular integral equations with a logarithmic singularity in their kernels and of two-dimensional singular integral equations with 1/ r singularity in their kernels. The generalization of the technique to several more complicated cases is also possible.