A fourth-order-accurate direct and inverse cauchy integral solver

A numerical procedure is presented for solving Cauchy integrals with fourth-order accuracy. The method, based on Spline Collocation Polynomials, is shown to be superior, by far, to a second-order-accurate finite difference approach. The evaluation of the integral (direct problem) and of the integrand as well (inverse problem) is considered. Several approaches are considered and some unexpected results for the case of the inverse problem are pointed out.