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1 Journal of Applied Mathematics and Computational Mechanics

1 2020

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On approximate conformal mapping of a disk and an annulus with radial and circular slits onto multiply connected domains

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Ivanshin P. N. , Shirokova E. A.

2020

tom Vol. 19, nr 2

73--84

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 m circular slits and n-m radial slits and an annulus with (m-1) circular slits and n-m radial slits onto an arbitrary given (n+1) multiply connected finite domain with a smooth boundary. The method is based on extension of the Lichtenstein-Gershgorin equation to a multiply connected domain. The proposed method is reduced to the solution of a linear system with unknown Fourier coefficients. The approximate mapping function has the form of a Cauchy integral. Numerical examples demonstrate that the proposed method is effective in computations.