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M. Giona and H. E. Roman, “Fractional Diffusion Equation for Transport Phenomena in Random Media,” Journal of Physics A, Vol. 185, No. 1-4, 1992, pp. 87-97.

has been cited by the following article:

• TITLE: Pseudo-Spectral Method for Space Fractional Diffusion Equation

  AUTHORS: Yiting Huang, Minling Zheng

  KEYWORDS: Riemann-Liouville Derivative; Pseudo-Spectral Method; Collocation Method; Fractional Diffusion Equation

  JOURNAL NAME: Applied Mathematics, Vol.4 No.11, November 5, 2013

  ABSTRACT: This paper presents a numerical scheme for space fractional diffusion equations (SFDEs) based on pseudo-spectral method. In this approach, using the Guass-Lobatto nodes, the unknown function is approximated by orthogonal polynomials or interpolation polynomials. Then, by using pseudo-spectral method, the SFDE is reduced to a system of ordinary differential equations for time variable t. The high order Runge-Kutta scheme can be used to solve the system. So, a high order numerical scheme is derived. Numerical examples illustrate that the results obtained by this method agree well with the analytical solutions.