Fast Implementation of Generalized Koebe’s Iterative Method
Abstract
1. Introduction
2. The Circular Ring with Circular Holes Map
3. Conformal Mappings from Unbounded Simply Connected Domains onto the Unit Disk
4. Conformal Mappings from Unbounded Doubly Connected Domains onto a Circular Ring
5. Generalized Koebe’s Iterative Method
5.1. Initializations
5.2. Iterations
5.2.1. Step I
5.2.2. Step II
5.3. The Interior Points
5.4. The Inverse Circular Map
5.5. Computational Complexity
6. Numerical Examples
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Method | Steps | Time (sec) | Roundness Error e(C) |
---|---|---|---|
Zeng et al. [22] | 5 | 486 | 0.143825 |
Our method | 2 | 1.62 | 0.009606 |
Example | m | n | Iterations | Time (s) |
---|---|---|---|---|
1 | 2 | 1024 | 12 | 6.20 |
2 | 3 | 1024 | 10 | 7.45 |
3 | 2 | 1024 | 50 | 25.84 |
4 | 99 | 1024 | 12 | 1259.67 |
5 | 3 | 4096 | 15 | 13.43 |
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Lee, K.W.; Murid, A.H.M.; Nasser, M.M.S.; Yeak, S.H. Fast Implementation of Generalized Koebe’s Iterative Method. Mathematics 2025, 13, 1920. https://doi.org/10.3390/math13121920
Lee KW, Murid AHM, Nasser MMS, Yeak SH. Fast Implementation of Generalized Koebe’s Iterative Method. Mathematics. 2025; 13(12):1920. https://doi.org/10.3390/math13121920
Chicago/Turabian StyleLee, Khiy Wei, Ali H. M. Murid, Mohamed M. S. Nasser, and Su Hoe Yeak. 2025. "Fast Implementation of Generalized Koebe’s Iterative Method" Mathematics 13, no. 12: 1920. https://doi.org/10.3390/math13121920
APA StyleLee, K. W., Murid, A. H. M., Nasser, M. M. S., & Yeak, S. H. (2025). Fast Implementation of Generalized Koebe’s Iterative Method. Mathematics, 13(12), 1920. https://doi.org/10.3390/math13121920