A comparison of numerical algorithms for solving cauchy singular integral equation

Abstract

Three different numerical algorithms for the solution of Cauchy type singular integral equations are compared by studying four test problems representing a variety of solutions expected. Numerical experiments show that Galerkin and collocation methods are comparable in accuracy either when the solution has no singularities at the end points or when these are present they are taken care by suitably chosen trial functions. Further, the dual quadrature collocation method introduced by Ioakimidis is seen to be equivalent to the conventional collocation scheme.