On the Convergence of Some Approximate Methods of Conformal Mapping

A method was given in Ellacott (1978) for determining approximately the conformal mapping of a Jordan region on to a disc. Some results on the convergence of this method are given, which can be used to prove the result (conjectured in Ellacott, 1978) that if the boundary curve is analytic, then conv...

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Bibliographic Details
Published in:IMA journal of numerical analysis 1981-04, Vol.1 (2), p.185-192
Main Author: ELLACOTT, S. W.
Format: Article
Language:English
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Summary:A method was given in Ellacott (1978) for determining approximately the conformal mapping of a Jordan region on to a disc. Some results on the convergence of this method are given, which can be used to prove the result (conjectured in Ellacott, 1978) that if the boundary curve is analytic, then convergence is uniform. The corresponding result is also proved for the Bergman and Szegō Kernel methods with polynomial basis functions. (The result is already known for the Szegö Kernel method, but a different proof is given.) Also discussed is the use of rational basis functions for the Bergman Kernel method.
ISSN:0272-4979
1464-3642
DOI:10.1093/imanum/1.2.185