MALAYSIAN MATHEMATICAL SCIENCES SOCIETY A Brief Overview of Fornberg-like Methods for Conformal Mapping of Simply and Multiply Connected Regions

Dedicated to the memory of Mohamad Rashidi Md. Razali Abstract. We give simplified derivations of Fornberg-like methods for conformal mapping of simply and multiply connected regions. The computational domains are circular domains and the derivations are based on Fourier series leading to conditions for analytic extension of boundary values to the computational domain. Linearization of these conditions with respect to the boundary correspondences and conformal moduli lead to Newton methods for approximating the mapping function. The linear systems can be solved by the conjugate gradient method