Improved Rotated Finite Difference Method for Solving Fractional Elliptic Partial Differential Equations
Keywords:
Rotated Finite Difference Approximation Method, Fractional Elliptic Partial Differential Equations.Abstract
Real life problems with fractional partial differential equations (FPDE's) are of great importance, since fractional differential equations accumulate the whole information of the function in a weighted form. This has many applications in physics, chemistry, engineering, etc. For that reason, we need a method for solving such equations, effectively, easy use and applied for different problems. The objective of this paper is to solve fractional elliptic partial differential equations, by using new accelerated version of rotated five point’s approximation method. Experiment results of the test problem are given in order to confirm the superiority of our proposed method.
References
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[5] A. M. Saeed, N. H. M. Ali, “On the Convergence of the Preconditioned Group Rotated Iterative Methods In The Solution of Elliptic PDEs”, Applied Mathematics &Information Sciences, vol. 5(1), pp. 65-73, 2011.
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[12] K. B. oldham, J. Spanier, The Fractional Calculus, Academic Press, New York, USA, 1974.
[2] A. Gunawardena, S. Jain, L. Snyder, ”Modified iterative methods for consistent linear systems”. Linear Algebra Appl.vol. 154/156, pp 123–143, 1991.
[3] A. Ibrahim and A. R. Abdullah, “Solving the Two Dimensional Diffusion Equation by the Four Point Explicit Decoupled Group (EDG) Iterative Method”. ,International Journal of Comp. Math. vol. 58, pp 253-263, 1994.
[4] A. M. Saeed and N. H. M. Ali, “Preconditioned Modified Explicit Decoupled Group Method In The Solution Of Elliptic PDEs”. Applied Mathematical Sciences.vol. 4 (24), pp. 1165-1181, 2010.
[5] A. M. Saeed, N. H. M. Ali, “On the Convergence of the Preconditioned Group Rotated Iterative Methods In The Solution of Elliptic PDEs”, Applied Mathematics &Information Sciences, vol. 5(1), pp. 65-73, 2011.
[6] S. I. Muslih, O. P. Agrawal, “Riesz Fractional Derivatives and Dimensional Space”, Int J Theor Phys, vol. 49(2), pp. 270-275, 2010.
[7] J. Hristov, “Approximate Solutions to Fractional Subdiffusion Equations”, European Physical Journal, vol. 193(1) pp. 229-243, 2011.
[8] V. D. Beibalaev, P. Ruslan, Meilanov, “The Dirihlet Problem for The Fractional Poisson’s Equation With Caputo Derivatives: Afinite Difference Approximation and A Numerical Solution”, Thermal Science, vol. 16(2), pp.385-394, 2012.
[9] Z. B. Li, J. H. He, “Fractional Complex Transform for Fractional Differential Equations”, Mathematical and Computational Applications, vol. 15(5), pp. 970-973, 2010.
[10] R. Metzler, J. Klafter, “The Random Walk’s Guide to Anomalous Diffusion: A Fractional Dynamics Approach”. Phys. Rep., vol.339(1) , pp.1-77, 2000.
[11] V. M. Goloviznin, I. A. Korotkin, “Methods of the Numerical Solutions Some One-Dimensional Equations with Fractional Derivatives”, Differential Equations, vol.42(7), pp. 21-130, 2006.
[12] K. B. oldham, J. Spanier, The Fractional Calculus, Academic Press, New York, USA, 1974.
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Published
2016-10-21
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Saeed, A. M. (2016). Improved Rotated Finite Difference Method for Solving Fractional Elliptic Partial Differential Equations. American Scientific Research Journal for Engineering, Technology, and Sciences, 26(1), 261–270. Retrieved from https://asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/2216
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