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

• Main Authors: Murid, Ali Hassan Mohamed, Laey, Nee Hu, Mohd. Nor, Mohamad
• Format: Article
• Language: English; English
• Published: Department of Mathematics, Faculty of Science 2008
• Subjects: QA Mathematics
• Online Access: http://eprints.utm.my/id/eprint/9857/1/AliHassanMohamed2008_An_Integral_Equation_Method_for_Conformal.pdf; http://eprints.utm.my/id/eprint/9857/3/20082421.pdf; http://eprints.utm.my/id/eprint/9857/
• Institution: Universiti Teknologi Malaysia

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.