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 $lt$ 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. Keywords: Conformal mapping; integral equations; doubly connected regions; Neumann kernel.