Nurcan BAYKUŞ SAVAŞANERİL, Zeynep HACIOĞLU

Bernstein Series Approximation for Dirichlet Problem

The basic aim of this paper is to present a novel efficient matrix approach for solving theDirichlet problem. The method converts the Dirichlet problem to a matrix equation, whichcorresponds to a system of linear algebraic equations. Error analysis is included to demonstratethe validity and applicability of the technique.

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Ahmadi, M.R., Adibi, H., “The Chebyshev tau technique for the solution of Laplace’s equation”, Appl. Math. Comput. 184(2): 895–900, (2007).
Baykus Savasaneril, N., Delibas, H., “Analytic solution for two-dimensional heat equation for an ellipse region”, New Trends in Mathematical Sciences, 4(1): 65–70, (2016).
Baykus Savasaneril, N., Delibas, H., “Analytic Solution for The Dirichlet Problem in 2-D”, J. Comput. Theor. Nanosci. 15(2): 611–615, (2018).
Hacioglu, Z., Baykus Savasaneril N., Kose, H., “Solution of Dirichlet problem for a square region in terms of elliptic functions”, New Trends in Mathematical Sciences, 3(4): 98–103, (2015).
Isik O.R., Sezer, M., Güney, Z., “Bernstein series solution of linear second-order partial differential equations with mixed conditions”, Math. Methods Appl. Sci. 37: 609–619, (2014).
Kurul, E., Baykus Savasaneril, N., “Solution of the two-dimensional heat equation for a rectangular plate”, New Trends in Mathematical Sciences, 3(4): 76–82, (2015).
Kong, W., Wu, X., “Chebyshev tau matrix method for Poisson-type equations in irregular domain”, J. Comput. Appl. Math. 228(1): 158–167, (2009).
Tamsir, M., Acan, O., Kumar, J., Singh, A.K., “Numerical Study of Gas Dynamics Equation arising in shock fronts”, Asia Pacific J. Eng. Sci. Technol. 2: 17–25, (2016).
Kurt, N., Sezer, M., Çelik, A., “Solution of Dirichlet problem for a rectangular region in terms of elliptic functions”, Int. J. Comput. Math. 81(11): 1417–1426, (2004).
Kurt, N., Sezer, M., “Solution of Dirichlet problem for a triangle region in terms of elliptic functions”, Appl. Math. Comput. 182(1): 73–78, (2006).
Kurt, N., “Solution of the two-dimensional heat equation for a square in terms of elliptic functions”, J. Franklin Inst. 345(3): 303–317, (2007).
Sezer, M., “Chebyshev polynomial approximation for Dirichlet problem. Journal of Faculty of Science Ege University Series A, 12(2): 69–77, (1989).
Yuksel, G., Isik, O.R., Sezer, M., “Error analysis of the Chebyshev collocation method for linear second-order partial differential equations”, Int. J. Comput. Math. 92(10): 2121–2138, (2014).
Yüksel, G., “Chebyshev polynomials solutions of second order linear partial differential equations”, Phd. Thesis, Muğla University Institute of Science, Muğla, 1-106 (2011).