The perturbed Galerkin method for Cauchy singular integral equations with constant coefficients

摘要

We have considered the numerical solution of Cauchy singular integral equations with constant coefficients via a polynomial based Galerkin method. L2 and uniform convergence results are proved under Hölder continuity conditions on the kernel and right hand side and taking into account the quadrature errors produced when inner products are replaced by numerical quadratures. These results generalize those of Miel, who considered only the case of equations of the first kind with index 0.