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On the numerical solutions for the fractional diffusion equation. (English) Zbl 1221.65263
Summary: 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.
MSC:
65M70Spectral, collocation and related methods (IVP of PDE)
35R11Fractional partial differential equations
26A33Fractional derivatives and integrals (real functions)
35K20Second order parabolic equations, initial boundary value problems
45K05Integro-partial differential equations
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