A reparameterisation method to determine conformal maps
type: Item
instance of: scholarly article
title: A reparameterisation method to determine conformal maps
zbMATH Open document ID: 0586.30010
DOI: 10.1016/0377-0427(86)90136-6
author: Hans-Peter Hoidn
published in: Journal of Computational and Applied Mathematics
publication date: 1986-01-01T00:00:00Z
review text: A conformal mapping of a simply connected Jordan region G onto the unit disk is constructed by computing the boundary correspondence. For this purpose the author uses the Symn integral equation as the main tool for his construction. The new idea in this paper is to construct a sufficiently smooth boundary representation of the given region by using a theorem of \textit{R. S. Lehman} [Pac. J. Math. 7, 1437-1449 (1957; Zbl 0087.289)]. The boundary representation is piecewise between occurring corners of the boundary. The method is applied to various test examples in which the given region is a circular sector where the opening angles are \(\frac{\pi}{2}\) and \(\frac{3\pi}{2}\). The examples show that in order to obtain high precision one has to take over hundred parameters into account.
Mathematics Subject Classification ID: 30C30
Mathematics Subject Classification ID: 65R20
zbMATH DE Number: 3939649
zbMATH Keywords: Symn integral equation
reviewed by: Gerhard Opfer
MaRDI profile type: Publication
full work available at URL: 0377-0427(86)90136-6
OpenAlex ID: W2071152756
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description: scientific article; zbMATH DE number 3939649