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

Ali Hassan Mohamed Murid, and Hu, Laey Nee, and Mohd Nor Mohamad, (2008) An Integral Equation Method for Conformal Mapping of Doubly Connected Regions Involving the Neumann Kernel. Matematika, 24 (2). pp. 99-111. ISSN 01278274

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Official URL: http://www.fs.utm.my/matematika/images/stories/matematika/20082421.pdf

Affiliations

Universiti Teknologi Malaysia, Faculty of Science, Dept. of Mathematics
Universiti Teknologi Malaysia, Faculty of Science, Dept. of Mathematics
Universiti Teknologi Malaysia, Faculty of Science, Dept. of Mathematics

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.

Item Type:Journal
Keywords:Conformal mapping; integral equations; doubly connected regions; Neumann kernel.
Subjects:Q Science, Computer Science
L Education
ID Code:5377

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