Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 16, Issue 6, Pages 2535-2542Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2010.09.007
Keywords
Finite difference method; Fractional diffusion equation; Chebyshev polynomials; Caputo derivative
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Fractional differential equations have recently been applied in various area of engineering, science, finance, applied mathematics, bio-engineering and others. However, many researchers remain unaware of this field. In this paper, an efficient numerical method for solving the fractional diffusion equation (FDE) is considered. The fractional derivative is described in the Caputo sense. The method is based upon Chebyshev approximations. The properties of Chebyshev polynomials are utilized to reduce FDE to a system of ordinary differential equations, which solved by the finite difference method. Numerical simulation of FDE is presented and the results are compared with the exact solution and other methods. (C) 2010 Elsevier B.V. All rights reserved.
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