An iterative method for the conformal mapping of doubly connected regions
type: Item
instance of: scholarly article
title: An iterative method for the conformal mapping of doubly connected regions
zbMATH Open document ID: 0577.30009
DOI: 10.1016/0377-0427(86)90131-7
author: Rudolf Wegmann
published in: Journal of Computational and Applied Mathematics
publication date: 1986-01-01T00:00:00Z
review text: From author's abstract: An iterative method is described for the determination of the conformal mapping of a circular annulus \(R_ q:=\{z:q<| z| <1\}\) onto a doubly connected region G with smooth boundary curves. The method is analogous to the method for simply connected regions. It requires in each step the solution of a Riemann- Hilbert problem on \(R_ q\). This problem can be solved explicitly in terms of a generalized conjugation operator K. If the boundary curves of G admit parametrizations by functions \(\eta_{\nu}\) with second derivatives which are Hölder continuous with exponent \(\mu\), \(0<\mu \leq 1\), then the method converges locally in the Sobolev space W of \(2\pi\)- periodic absolutely continuous functions with square-integrable derivatives. The order of convergence is at least \(1+\mu\). The convergence is quadratic if the \(\eta_{\nu}\) have Lipschitz-continuous second derivatives. The results of some test calculations are reported and compared with results of calculations with the method of Theodorsen- Garrick.
Mathematics Subject Classification ID: 30C30
zbMATH DE Number: 3923052
zbMATH Keywords: Riemann-Hilbert problem
zbMATH Keywords: method of Theodorsen-Garrick
reviewed by: Dieter Gaier
MaRDI profile type: Publication
full work available at URL: 0377-0427(86)90131-7
OpenAlex ID: W2000209770
cites work: Q4104185
cites work: A Numerical Method for Conformal Mapping of Doubly Connected Regions
cites work: Konstruktive Methoden der konformen Abbildung
cites work: Fast Fourier Methods in Computational Complex Analysis
cites work: Q5332327
cites work: Q4334484
cites work: An iterative method for conformal mapping
cites work: Convergence proofs and error estimates for an iterative method for conformal mapping
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description: scientific article; zbMATH DE number 3923052