Numerical conformal mapping methods for exterior regions with corners
type: Item
instance of: scholarly article
title: Numerical conformal mapping methods for exterior regions with corners
zbMATH Open document ID: 0788.30006
author: A. Elcrat
author: T. K. DeLillo
published in: Journal of Computational Physics
publication date: 1994-03-17T00:00:00Z
review text: Let \(C\) be a piecewise analytic Jordan curve, and assume that \(f\) maps the exterior of \(C\) conformally onto \(\{w:| w |>1\}\) such that \(f(z)=az+a_ 0+{a_ 1 \over z}+\cdots\). Let \(z=z(\sigma)\) \((0 \leq \sigma \leq L)\) be the representation of \(C\) in terms of arc length, and let \(\theta=\theta(\sigma)=\arg f(z(\sigma))\) be the boundary correspondence between \(C\) and \(\{w:| w |=1\}\). Timman (1952) had given an equation for \(\sigma=\sigma(\theta)\) which the authors transform into a nonlinear integro-differential equation for \(\theta(\sigma)\) involving the curvature of \(C\). This is then solved by iteration, and the new method compared numerically with several other methods.
Mathematics Subject Classification ID: 30C30
zbMATH DE Number: 516906
reviewed by: Dieter Gaier
MaRDI profile type: Publication
full work available at URL: jcph.1993.1175
OpenAlex ID: W2060546305
DOI: 10.1006/JCPH.1993.1175
Recommended article: Numerical conformal mapping of exterior domains
Recommended article: A Comparison of some Numerical Conformal Mapping Methods for Exterior Regions
Recommended article: Numerical Conformal Mapping Methods for Simply and Doubly Connected Regions
Recommended article: Q4668882
Recommended article: Numerical techniques for conformal mapping onto a rectangle
Recommended article: Numerical conformal mapping of multiply connected domains to regions with circular boundaries
Recommended article: A Numerical Method for Conformal Mapping of Doubly Connected Regions
Recommended article: Q3322358
Recommended article: Numerical conformal mapping for exterior regions via the Kerzman-Stein kernel
description: scientific article; zbMATH DE number 516906