TAILIEUCHUNG - Pseudospectral operational matrix for numerical solution of single and multiterm time fractional diffusion equation

This paper presents a new numerical approach to solve single and multiterm time fractional diffusion equations. In this work, the space dimension is discretized to the Gauss−Lobatto points. We use the normalized Grunwald approximation for the time dimension and a pseudospectral successive integration matrix for the space dimension. | Turk J Math (2016) 40: 1118 – 1133 ¨ ITAK ˙ c TUB ⃝ Turkish Journal of Mathematics doi: Research Article Pseudospectral operational matrix for numerical solution of single and multiterm time fractional diffusion equation Saeid GHOLAMI1 , Esmail BABOLIAN1,2 , Mohammad JAVIDI3,∗ Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran 2 Faculty of Mathematical Sciences and Computer, Kharazmy University, Tehran, Iran 3 Department of Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran 1 Received: • Accepted/Published Online: • Final Version: Abstract: This paper presents a new numerical approach to solve single and multiterm time fractional diffusion equations. In this work, the space dimension is discretized to the Gauss − Lobatto points. We use the normalized Grunwald approximation for the time dimension and a pseudospectral successive integration matrix for the space dimension. This approach shows that with fewer numbers of points, we can approximate the solution with more accuracy. Some examples with numerical results in tables and figures displayed. Key words: Pseudospectral integration matrix, normalized Grunwald approximation, Gauss − Lobatto points, multiterm fractional diffusion equation 1. Introduction In recent years, due to the accuracy of fractional differential equations in describing a variety of engineering and physics fields, such as kinetics [23, 24, 26, 27, 34, 35, 39], solid mechanics [32], quantum systems [38], magnetic plasma [25], and economics [3], many researchers are interested in fractional calculus. In [39] the concepts of fractional kinetic, such as particle dynamics in different potentials, particle advection in fluids, plasma physics, fusion devices, and quantum optics, were discussed. The fractional kinetics of the diffusion, diffusion-advection, and Fokker− Planck type were .

• Toán học
• Pseudospectral integration matrix
• Normalized Grunwald approximation
• Gauss−Lobatto points
• Multiterm fractional diffusion equation
• Space dimension
• Science Fiction
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• Space Tug
• Operation Terror
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• Lecture Linear algebra
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• Definition and examples
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