An integral equation method for conformal mapping of doubly connected regions involving the neumann kernel

Abstract

We present an integral equation method for conformal mapping of doubly connected regions onto a unit disc with a circular slit of radius µ < 1. Our theoretical development is based on the boundary integral equation for conformal mapping of doubly connected region derived by Murid and Razali [15]. In this paper, using the boundary relationship satisfied by the mapping function, a related system of integral equations via Neumann kernel is constructed. For numerical experiment, the integral equation is discretized which leads to a system of linear equations, where µ is assumed known. Numerical implementation on a circular annulus is also presented.