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Zbl 1159.30007
Nasser, Mohamed M.S.
A boundary integral equation for conformal mapping of bounded multiply connected regions. (English)
[J] Comput. Methods Funct. Theory 9, No. 1, 127-143 (2009). ISSN 1617-9447; ISSN 2195-3724/e

Summary: A boundary integral method is presented for constructing approximations to the mapping functions of bounded multiply connected regions to the standard canonical slit domains given by {\it Z. Nehari} [``Conformal Mapping", (International Series in Pure and Applied Mathematics) New York-Toronto- London: McGraw-Hill Book Company, Inc. VIII, 396 p. (1952; Zbl 0048.31503)]. 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.

MSC 2000:: *30C30 Numerical methods in conformal mapping theory
30E25 Boundary value problems, complex analysis
45B05 Fredholm integral equations

Keywords: numerical conformal mapping; multiply connected regions; generalized Neumann kernel; Riemann-Hilbert problem

Citations: Zbl 0048.31503

Cited in: Zbl 1198.30009

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