- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 948564, 8 pages
Analysis of the Block-Grid Method for the Solution of Laplace's Equation on Polygons with a Slit
Department of Mathematics, Eastern Mediterranean University, Gazimagusa, Cyprus, 095 Mersin 10, Turkey
Received 22 April 2013; Accepted 30 April 2013
Academic Editor: Allaberen Ashyralyev
Copyright © 2013 S. Cival Buranay. 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.
- Z. C. Li, Combined Methods for Elliptic Problems with Singularities, Interfaces and Infinities, Kluwer Academic, London, UK, 1998.
- A. A. Dosiyev, “A block-grid method for increasing accuracy in the solution of the Laplace equation on polygons,” Russian Academy of Sciences, vol. 45, no. 2, pp. 396–399, 1992.
- A. A. Dosiyev, “A block-grid method of increased accuracy for solving Dirichlet's problem for Laplace's equation on polygons,” Computational Mathematics and Mathematical Physics, vol. 34, no. 5, pp. 591–604, 1994.
- A. A. Dosiyev, “The high accurate block-grid method for solving Laplace's boundary value problem with singularities,” SIAM Journal on Numerical Analysis, vol. 42, no. 1, pp. 153–178, 2004.
- A. A. Dosiyev and S. Cival, “A difference-analytical method for solving Laplace's boundary value problem with singularities,” in Proceedings of Conference on Applications of Dynamical Systems, pp. 339–360, Antalya, Turkey, July 2004.
- A. A. Dosiyev and S. C. Buranay, “A fourth order accurate difference-analytical method for solving Laplace's boundary value problem with singularities,” in Mathematical Methods in Engineers, K. Tas, J. A. T. Machado, and D. Baleanu, Eds., pp. 167–176, Springer, Berlin, Germany, 2007.
- E. A. Volkov, “An exponentially converging method for solving Laplace's equation on polygons,” Mathematics of the USSR-Sbornik, vol. 37, no. 3, pp. 295–325, 1980.
- E. A. Volkov, Block Method for Solving the Laplace Equation and Constructing Conformal Mappings, CRC Press, Boca Raton, Fla, USA, 1994.
- N. M. Wigley, “An efficient method for subtracting off singularities at corners for Laplace's equation,” Journal of Computational Physics, vol. 78, no. 2, pp. 369–377, 1988.
- G. J. Fix, S. Gulati, and G. I. Wakoff, “On the use of singular functions with finite element approximations,” Journal of Computational Physics, vol. 13, pp. 209–228, 1973.
- W. Wasow, “On the truncation error in the solution of Laplace's equation by finite differences,” Journal of Research of the National Bureau of Standards, vol. 48, pp. 345–348, 1952.
- S. E. Romanova, “An efficient method for the approximate solution of the Laplace difference equation on rectangular domains,” Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, vol. 23, no. 3, pp. 660–673, 1983.
- A. A. Dosiyev and S. C. Buranay, “On solving the cracked-beam problem by block method,” Communications in Numerical Methods in Engineering with Biomedical Applications, vol. 24, no. 11, pp. 1277–1289, 2008.