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A boundary integral equation for conformal mapping of bounded multiply connected regions. (English) Zbl 1159.30007
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 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.

30C30Numerical methods in conformal mapping theory
30E25Boundary value problems, complex analysis
45B05Fredholm integral equations
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