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This article is cited in 2 scientific papers (total in 2 papers)
The approximate conformal mapping onto multiply connected domains
D. F. Abzalilov, E. A. Shirokova Kazan Federal University, 18 Kremlyovskaya str Kazan, 420008, Russia
Abstract:
The method of boundary curve reparametrization is generalized to the case of multiply connected domains. We construct the approximate analytical conformal mapping of the unit disk with $N$ circular slits or an annulus with $(N-1)$ circular slits onto an arbitrary $(N+1)$ multiply connected finite domain with a smooth boundary. The method is based on the solution of the Fredholm equation. This solution is reduced to the solution of a linear system with unknown Fourier coefficients. The approximate mapping function has the form of a set of Laurent polynomials in the set of annular regions The method is easily computable.
Keywords:
conformal mapping, multiply connected domain, Fredholm integral equation.
Received: 30.07.2018 Revised: 20.12.2018 Accepted: 19.12.2018
Citation:
D. F. Abzalilov, E. A. Shirokova, “The approximate conformal mapping onto multiply connected domains”, Probl. Anal. Issues Anal., 8(26):1 (2019), 3–16
Linking options:
https://www.mathnet.ru/eng/pa254 https://www.mathnet.ru/eng/pa/v26/i1/p3
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Abstract page: | 168 | Full-text PDF : | 67 | References: | 16 |
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