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Numerical conformal mapping of bounded multiply connected regions by an integral equation method. (English) Zbl 1198.30008
The authors continue their studies of numerical experiments on conformal mappings of multiply connected domains [same authors, Int. J. Pure Appl. Math. 51, No. 4, 589–608 (2009; Zbl 1178.30004)]. Let \(\Omega\) be a Jordan domain of \(n+1\) connectivity with a sufficiently regular boundary, let \(f\) be a suitably normalized conformal map of \(\Omega\) onto an annulus with concentric circular slits. Given boundary values of \(f\), they derive an integral equation satisfied by \(f'\). Then they consider the cases \(n= 1\), \(n= 2\), and they present numerical examples which show the effectiveness of their method.

MSC:
30C30 Schwarz-Christoffel-type mappings
65R20 Numerical methods for integral equations
65E05 General theory of numerical methods in complex analysis (potential theory, etc.)
30C40 Kernel functions in one complex variable and applications
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