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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 864865, 11 pages
A Fourth-Order Block-Grid Method for Solving Laplace's Equation on a Staircase Polygon with Boundary Functions in
Department of Mathematics, Eastern Mediterranean University, Gazimagusa, North Cyprus, Mersin 10, Turkey
Received 30 April 2013; Accepted 11 May 2013
Academic Editor: Allaberen Ashyralyev
Copyright © 2013 A. A. Dosiyev and 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 Publishers, Dordrecht, The Netherlands, 1998.
- 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, “A block-grid method for increasing accuracy in the solution of the Laplace equa-tion 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 forLaplace's equation on polygons,” Computational Mathematics and Mathematical Physics, vol. 34, no. 5, pp. 591–604, 1994.
- A. A. Dosiyev and S. Cival, “A difference-analytical method for solving Laplace's boundary valueproblem with singularities,” in Proceedings of Conference Dynamical Systems and Applications, pp. 339–360, Antalya, Turkey, July 2004.
- A. A. Dosiyev and S. Cival, “A combined method for solving Laplace's boundary value problem with singularities,” International Journal of Pure and Applied Mathematics, vol. 21, no. 3, pp. 353–367, 2005.
- 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, 2007.
- A. A. Dosiyev, S. Cival Buranay, and D. Subasi, “The block-grid method for solving Laplace's equation on polygons with nonanalytic boundary conditions,” Boundary Value Problems, Article ID 468594, 22 pages, 2010.
- A. A. Dosiyev, S. C. Buranay, and D. Subasi, “The highly accurate block-grid method in solving Laplace's equation for nonanalytic boundary condition with corner singularity,” Computers & Mathematics with Applications, vol. 64, no. 4, pp. 616–632, 2012.
- E. A. Volkov, “Approximate solution of Laplace's equation by the block method on polygons undernonanalytic boundary conditions,” Proceedings of the Steklov Institute of Mathematics, no. 4, pp. 65–90, 1993.
- E. A. Volkov, “Differentiability properties of solutions of boundary value problems for the Laplaceand Poisson equations on a rectangle,” Proceedings of the Steklov Institute of Mathematics, vol. 77, pp. 101–126, 1965.
- A. A. Samarskii, The Theory of Difference Schemes, vol. 240 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 2001.
- A. A. Dosiyev, “On the maximum error in the solution of Laplace equation by finite difference method,” International Journal of Pure and Applied Mathematics, vol. 7, no. 2, pp. 229–241, 2003.
- A. A. Dosiyev, “A fourth order accurate composite grids method for solving Laplace's boundary value problems with singularities,” Computational Mathematics and Mathematical Physics, vol. 42, no. 6, pp. 867–884, 2002.
- 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 for Constructing Conformal Mappings, CRC Press, Boca Raton, Fla, USA, 1994.
- 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.