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Fast Implementation of Generalized Koebe’s Iterative Method

Author

Listed:
  • 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)

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.

Suggested Citation

  • Khiy Wei Lee & Ali H. M. Murid & Mohamed M. S. Nasser & Su Hoe Yeak, 2025. "Fast Implementation of Generalized Koebe’s Iterative Method," Mathematics, MDPI, vol. 13(12), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:12:p:1920-:d:1674808
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