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An Integral Equation Method for Conformal Mapping of Doubly Connected Regions Involving the Neumann Kernel

Author(s): Ali Hassan Mohamed Murid | Laey-Nee Hu | Mohd Nor Mohamad

Journal: Matematika
ISSN 0127-8274

Volume: 24;
Issue: 2;
Start page: 99;
Date: 2008;
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Keywords: Conformal mapping | integral equations | doubly connected regions | Neumann kernel.

We present an integral equation method for conformal mapping of doublyconnected 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.

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