Numerical solution of systems of Cauchy singular integral equations with constant coefficients

摘要

This paper deals with the numerical solution of a class of systems of Cauchy singular integral equations with constant coefficients. The proposed procedure consists of two basic steps: the first one is to consider a modified problem equivalent to the original one under suitable conditions, the second one is to approximate its solution by means of a vector of polynomial functions. Such array is constructed by applying a quadrature type method, based on Gaussian rules, that leads to solve a determined and well conditioned linear system. The convergence and stability of the method are proved in weighted L2 spaces. Some numerical tests are also shown.