Geodesic
The approximate conformal mapping onto multiply connected domains
Problemy analiza, Tome 8 (2019) no. 1, pp. 3-16.

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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. 
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D. F. Abzalilov; E. A. Shirokova. The approximate conformal mapping onto multiply connected domains. Problemy analiza, Tome 8 (2019) no. 1, pp. 3-16. http://geodesic.mathdoc.fr/item/PA_2019_8_1_a0/

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