Discrete projection methods for cauchy singular integral equations with constant coefficients

摘要

We consider proving the mean-square and uniform convergence of various discrete Galerkin and collocation methods for Cauchy singular integral equations with constant coefficients. For Galerkin's method the convergence rates improve those given in an earlier paper, while for collocation methods the results appear to be new. In particular, we consider product quadrature methods for equations with discontinuous coefficients, and develop and prove the convergence of a new algorithm for equations of the first kind with index zero and logarithmically singular kernels.