Geodesic
A Brief Overview of Fornberg-like Methods for Conformal Mapping of Simply and Multiply Connected Regions
Bulletin of the Malaysian Mathematical Society, Tome 26 (2003) no. 1 
Noureddine Benchama; Thomas K. DeLillo. A
                        Brief Overview of Fornberg-like Methods for Conformal
                        Mapping of Simply and Multiply Connected Regions. Bulletin of the Malaysian Mathematical Society, Tome 26 (2003) no. 1. http://geodesic.mathdoc.fr/item/BMMS_2003_26_1_a6/
@article{BMMS_2003_26_1_a6,
     author = {Noureddine Benchama and Thomas K. DeLillo},
     title = {A
                        {Brief} {Overview} of {Fornberg-like} {Methods} for {Conformal
}                        {Mapping} of {Simply} and {Multiply} {Connected} {Regions}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2003},
     volume = {26},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2003_26_1_a6/}
}
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                        Mapping of Simply and Multiply Connected Regions
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                        Brief Overview of Fornberg-like Methods for Conformal
                        Mapping of Simply and Multiply Connected Regions
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Voir la notice de l'article provenant de la source BMMS

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.