Mittag-Leffler-Pade approximations for the numerical solution of space and time fractional diffusion equations

  • Authors

    • Abdollah Borhanifar Faculty of Mathematical Science, University of Mohaghegh Ardabili, Ardabil,
    • Sohrab Valizadeh Faculty of Mathematical Science, University of Mohaghegh Ardabili, Ardabil,
    2015-09-21
    https://doi.org/10.14419/ijamr.v4i4.4340
  • Fractional diffusion equation, Pade approximation, finite difference method, Mittag-Leffler function, stability and convergence.

  • Anomalous diffusion and non-exponential relaxation patterns can be described by a space - time fractional diffusion equation. This paper aims to present a Pade approximation for Mittag-Leffler function mixed finite difference method to develop a numerical method to obtain an approximate solution for the space and time fractional diffusion equation. The truncation error of the method is theoretically analyzed. It is proved that the numerical proposed method is unconditionally stable from the matrix analysis point of view. Finally, some numerical results are given, which demonstrate the efficiency of the approximate scheme.

    Author Biography

    • Abdollah Borhanifar, Faculty of Mathematical Science, University of Mohaghegh Ardabili, Ardabil,
      • I got my PhD from Moscow University in 2004 on nonlinear PDE. I have had teaching/research position in the university of Mohaghegh Ardabili university from1997 and now I am the chairman of science faculty of the university. I have couple publication in some scientific journals. At now I associate degree.

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    Borhanifar, A., & Valizadeh, S. (2015). Mittag-Leffler-Pade approximations for the numerical solution of space and time fractional diffusion equations. International Journal of Applied Mathematical Research, 4(4), 466-480. https://doi.org/10.14419/ijamr.v4i4.4340