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A Boundary Integral Equation for Conformal Mapping of Bounded Multiply Connected Regions

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Abstract

A boundary integral method is presented for constructing approximations to the mapping functions of bounded multiply connected regions to the standard canonical slits domains given by Nehari [11]. The method is based on expressing the mapping function in terms of the solution of a Riemann-Hilbert problem which can be solved by a uniquely solvable boundary integral equation with the generalized Neumann kernel. Three numerical examples are presented to show the effectiveness of the present method.

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Authors and Affiliations

  1. Faculty of Science, Department of Mathematics, Ibb University, P.O.Box 70270, Ibb, Yemen

    Mohamed M. S. Nasser

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  1. Mohamed M. S. Nasser
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Correspondence to Mohamed M. S. Nasser.

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Nasser, M.M.S. A Boundary Integral Equation for Conformal Mapping of Bounded Multiply Connected Regions. Comput. Methods Funct. Theory 9, 127–143 (2009). https://doi.org/10.1007/BF03321718

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