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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 293765, 29 pages
Conformal Mapping of Unbounded Multiply Connected Regions onto Canonical Slit Regions
1Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Johor, 81310 Johor Bahru, Malaysia
2Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia, Johor, 81310 Johor Bahru, Malaysia
3Faculty of Science and Technology, Universiti Sains Islam Malaysia, Negeri Sembilan 71800, Bandar Baru Nilai, Malaysia
4Department of Mathematics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia
5Department of Mathematics, Faculty of Science, Ibb University, P. O. Box 70270, Ibb, Yemen
Received 22 May 2012; Accepted 18 July 2012
Academic Editor: Matti Vuorinen
Copyright © 2012 Arif A. M. Yunus et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- V. V. Andreev, D. Daniel, and T. H. McNicholl, “Technical report: Computation on the extended complex plane and conformal mapping of multiply-connected domains,” in Proceedings of the 5th International Conference on Computability and Complexity in Analysis (CCA '08), vol. 221 of Electronic Notes in Theoretical Computer Science, pp. 127–139, Elsevier, 2008.
- G. C. Wen, Conformal Mapping and Boundary Values Problems, vol. 106 of Translations of Mathematical Monographs, American Mathematical Society, Providence, RI, USA, 1992, English translation of Chinese edition, 1984.
- Z. Nehari, Conformal Mapping, Dover, New York, NY, USA, 1952.
- P. Henrici, Applied and Computational Complex Analysis. Vol. 3, Pure and Applied Mathematics, John Wiley & Sons, New York, NY, USA, 1986.
- L. N. Trefethen, Ed., Numerical Conformal Mapping, North-Holland, Amsterdam, The Netherlands, 1986.
- K. Amano, “A charge simulation method for numerical conformal mapping onto circular and radial slit domains,” SIAM Journal on Scientific Computing, vol. 19, no. 4, pp. 1169–1187, 1998.
- T. K. DeLillo, T. A. Driscoll, A. R. Elcrat, and J. A. Pfaltzgraff, “Radial and circular slit maps of unbounded multiply connected circle domains,” Proceedings of The Royal Society of London Series A, vol. 464, no. 2095, pp. 1719–1737, 2008.
- A. H. M. Murid, Boundary integral equation approach for numerical conformal mapping [Ph.D. thesis], Universiti Teknologi Malaysia, 1999.
- A. H. M. Murid and M. R. M. Razali, “An integral equation method for conformal mapping of doubly connected regions,” Matematika, vol. 15, no. 2, pp. 79–93, 1999.
- A. H. M. Murid and L.-N. Hu, “Numerical experiment on conformal mapping of doubly connected regions onto a disk with a slit,” International Journal of Pure and Applied Mathematics, vol. 51, no. 4, pp. 589–608, 2009.
- M. M. S. Nasser, “A boundary integral equation for conformal mapping of bounded multiply connected regions,” Computational Methods and Function Theory, vol. 9, no. 1, pp. 127–143, 2009.
- M. M. S. Nasser, “Numerical conformal mapping via a boundary integral equation with the generalized Neumann kernel,” SIAM Journal on Scientific Computing, vol. 31, no. 3, pp. 1695–1715, 2009.
- M. M. S. Nasser, “Numerical conformal mapping of multiply connected regions onto the second, third and fourth categories of Koebe's canonical slit domains,” Journal of Mathematical Analysis and Applications, vol. 382, no. 1, pp. 47–56, 2011.
- A. W. K. Sangawi, A. H. M. Murid, and M. M. S. Nasser, “Linear integral equations for conformal mapping of bounded multiply connected regions onto a disk with circular slits,” Applied Mathematics and Computation, vol. 218, no. 5, pp. 2055–2068, 2011.
- A. W. K. Sangawi, A. H. M. Murid, and M. M. S. Nasser, “Annulus with circular slit map of bounded multiply connected regions via integral equation method,” Bulletin of Malaysian Mathematical Sciences Society. In press.
- A. W. K. Sangawi, A. H. M. Murid, and M. M. S. Nasser, “Circular slits map of bounded multiply connected regions,” Abstract and Applied Analysis, vol. 2012, Article ID 970928, 26 pages, 2012.
- A. W. K. Sangawi, A. H. M. Murid, and M. M. S. Nasser, “Parallel slits map of bounded multiply connected regions,” Journal of Mathematical Analysis and Applications, vol. 389, no. 2, pp. 1280–1290, 2012.
- R. Wegmann and M. M. S. Nasser, “The Riemann-Hilbert problem and the generalized Neumann kernel on multiply connected regions,” Journal of Computational and Applied Mathematics, vol. 214, no. 1, pp. 36–57, 2008.
- M. M. S. Nasser, A. H. M. Murid, M. Ismail, and E. M. A. Alejaily, “Boundary integral equations with the generalized Neumann kernel for Laplace's equation in multiply connected regions,” Applied Mathematics and Computation, vol. 217, no. 9, pp. 4710–4727, 2011.
- F. D. Gakhov, Boundary Value Problems, Translation edited by I. N. Sneddon, Pergamon Press, Oxford, UK, 1966, English translation of Russian edition, 1963.
- K. E. Atkinson, The Numerical Solution of Integral Equations of the Second Kind, vol. 4 of Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, Cambridge, UK, 1997.