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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 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. MSC 2010: 30C20, 45B05

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