Numerical conformal mapping of doubly connected regions onto a disc with a circular slit - Ali H.M. Murid,; Laey , Nee Hu; Mohd Nor Mohamad, (Penerbit ukm, 2008)

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An integral equation method based on the Neumann kernel for conformal mapping f(z) of doubly connected regions onto a unit disc with a circular slit of radius µ < 1 is presented. The theoretical development is based on the boundary integral equation for conformal mapping of doubly connected region in an earlier work of the authors. In this paper, a related system of integral equations is constructed that is satisfied by f '(z) and µ. For numerical experiment, the integral equation is discretised which leads to a system of nonlinear equations. The system obtained is solved simultaneously using Gauss-Newton method. Numerical implementation on a circular annulus is also presented