Fast Implementation of Generalized Koebe’s Iterative Method

Khiy Wei Lee, Ali H. M. Murid, Mohamed M. S. Nasser () and Su Hoe Yeak
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Khiy Wei Lee: Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia (UTM), Johor Bahru 81310, Johor, Malaysia
Ali H. M. Murid: Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia (UTM), Johor Bahru 81310, Johor, Malaysia
Mohamed M. S. Nasser: Department of Mathematics, Statistics & Physics, Wichita State University, Wichita, KS 67260-0033, USA
Su Hoe Yeak: Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia (UTM), Johor Bahru 81310, Johor, Malaysia

Mathematics, 2025, vol. 13, issue 12, 1-20

Abstract: Let G be a given bounded multiply connected domain of connectivity m + 1 bounded by smooth Jordan curves. Koebe’s iterative method is a classical method for computing the conformal mapping from the domain G onto a bounded multiply connected circular domain obtained by removing m disks from the unit disk. Koebe’s method has been generalized to compute the conformal mapping from the domain G onto a bounded multiply connected circular domain obtained by removing m − 1 disks from a circular ring. A fast numerical implementation of the generalized Koebe’s iterative method is presented in this paper. The proposed method is based on using the boundary integral equation with the generalized Neumann kernel. Several numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.

Keywords: Generalized Koebe’s iterative method; multiply connected domains; boundary integral equation method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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