Jacobi polynomial solutions of first kind integral equations for numerical conformal mapping

Abstract

A numerical method is described for the conformal mapping of simply connected domains whose boundaries contains sharp corner points. The method is based on a first kind integral equation formulation due to Wendland [15]. On each component analytic arc of the boundary, the dominant singularities of the unknown source density ν are incorporated in a Jacobi weight function w, so that ν/ w may be approximated by a finite Jacobi polynomial series. The coefficients in these series are determined by collocation. Numerical example illustrate the accuracy of the proposed technique.