An integral equation method for conformal mapping of doubly connected regions involving the neumann kernel - Murid, Ali Hassan Mohamed; Laey, Nee Hu; Mohd. Nor, Mohamad (Department of Mathematics, Faculty of Science, 2008)
We present an integral equation method for conformal mapping of doubly connected regions onto a unit disc with a circular slit of radius Âµ < 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 Âµ is assumed known. Numerical implementation on a circular annulus is also presented.