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We present a boundary integral equation method for the numerical conformal mappings and their inverses of bounded multiply connected regions onto circular and parallel slits regions. The method is based on two uniquely solvable boundary integral equations with Neumann-type and generalized Neumann kernels. These boundary integral equations are constructed from a boundary relationship satisfied by a function analytic on a multiply connected region. A method to calculate the inverse mapping functions from circular and parallel slits regions onto the original region is presented. Some numerical examples and numerical results with the graphical user interface are presented to illustrate the efficiency of the presented method.

Conformal mappings of bounded multiply connected regions onto circular and parallel slits regions and their inverses using a GUI