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On the numerical solutions for the fractional diffusion equation

✍ Scribed by M.M. Khader

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
501 KB
Volume
16
Category
Article
ISSN
1007-5704

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✦ Synopsis

a b s t r a c t 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.

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