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Abstract and Applied Analysis

Volume 2012 (2012), Article ID 293765, 29 pages

http://dx.doi.org/10.1155/2012/293765

## Conformal Mapping of Unbounded Multiply Connected Regions onto Canonical Slit Regions

^{1}Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Johor, 81310 Johor Bahru, Malaysia^{2}Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia, Johor, 81310 Johor Bahru, Malaysia^{3}Faculty of Science and Technology, Universiti Sains Islam Malaysia, Negeri Sembilan 71800, Bandar Baru Nilai, Malaysia^{4}Department of Mathematics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia^{5}Department 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.

#### Linked References

- 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. View at Publisher · View at Google Scholar - 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - 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. View at Google Scholar - 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. View at Google Scholar · View at Zentralblatt MATH - 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. View at Google Scholar · View at Zentralblatt MATH - 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - 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. View at Publisher · View at Google Scholar - 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. View at Publisher · View at Google Scholar · View at Scopus - 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - 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. View at Publisher · View at Google Scholar