Numerical conformal mapping of multiply connected regions onto the second, third and fourth categories of Koebe’s canonical slit domains. (English) Zbl 1227.30007

Nasser, Mohamed M. S.

J. Math. Anal. Appl. 382, No. 1, 47-56 (2011).

In his previous papers the author presented a boundary integral method to approximate conformal mappings from a multiply connected region onto the first category of Koebe’s canonical slit domains. The present article extends the author’s approach for numerical approximations of such conformal mappings onto the second, third and fourth categories of slit domains, namely: an annulus with spiral slits, a disk with spiral slits, a plane with spiral slits, a plane with straight slits.
The numerical method is based on a boundary integral equation which is uniquely solvable. The theoretical proposals are illustrated by three examples and many figures.

Reviewer: Dmitri V. Prokhorov (Saratov)

MSC:

30C20	Conformal mappings of special domains
30C30	Schwarz-Christoffel-type mappings

Keywords:

numerical conformal mapping; multiply connected region; generalized Neumann kernel

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