On the Comparison of Two Numerical Methods for Conformal Mapping

Let G be a simply connected domain in the t plane (t = x + iy), bounded by the three straight lines x = 0, y = 0, x = 1 and a Jordan arc with cartesian equation y = τ(x). Also, let g be the function which maps conformally a rectangle R onto G, so that the four corners of R are mapped onto those of G...

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Bibliographic Details
Published in:IMA journal of numerical analysis 1987-07, Vol.7 (3), p.261-282
Main Authors: GAIER, D., PAPAMICHAEL, N.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Sciences and techniques of general use
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Summary:Let G be a simply connected domain in the t plane (t = x + iy), bounded by the three straight lines x = 0, y = 0, x = 1 and a Jordan arc with cartesian equation y = τ(x). Also, let g be the function which maps conformally a rectangle R onto G, so that the four corners of R are mapped onto those of G. In this paper we show that the method considered in 1982 by Challis & Burley for determining approximations to g is equivalent to a special case of the well-known method of Garrick for the mapping of doubly connected domains. Hence, by using results already available in the literature, we provide some theoretical justification for the method of Challis & Burley.
ISSN:0272-4979
1464-3642
DOI:10.1093/imanum/7.3.261