Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation

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Abdollahy Zeynab; MAHMOUDI YAGHOUB; Salimi Shamloo Ali; Baghmisheh Mahdi

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Journal Paper

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Journal: Computational Methods for Differential Equations Year:2022 | Volume:10 | Issue:3 Page(s): 799-815

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Title

Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation

Author(s)

Abdollahy Zeynab | MAHMOUDI YAGHOUB | Salimi Shamloo Ali | Baghmisheh Mahdi | Issue Writer Certificate

Keywords

Fractional derivatives

Fractional diffusion equation

Riesz fractional derivative

Finite differences

Abstract

In this study, one explicit and one implicit finite difference scheme is introduced for the numerical solution of time-fractional Riesz space diffusion equation. The time derivative is approximated by the standard Gr¨, unwald Letnikov formula of order one, while the Riesz space derivative is discretized by Fourier transform-based algorithm of order four. The stability and convergence of the proposed methods are studied. It is proved that the implicit scheme is unconditionally stable, while the explicit scheme is stable conditionally. Some examples are solved to illustrate the efficiency and accuracy of the proposed methods. Numerical results confirm that the accuracy of present schemes is of order one.

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APA: Copy

Abdollahy, Zeynab, MAHMOUDI, YAGHOUB, Salimi Shamloo, Ali, & Baghmisheh, Mahdi. (2022). Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation. COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 10(3), 799-815. SID. https://sid.ir/paper/1057326/en

Vancouver: Copy

Abdollahy Zeynab, MAHMOUDI YAGHOUB, Salimi Shamloo Ali, Baghmisheh Mahdi. Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation. COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS[Internet]. 2022;10(3):799-815. Available from: https://sid.ir/paper/1057326/en

IEEE: Copy

Zeynab Abdollahy, YAGHOUB MAHMOUDI, Ali Salimi Shamloo, and Mahdi Baghmisheh, “Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation,” COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, vol. 10, no. 3, pp. 799–815, 2022, [Online]. Available: https://sid.ir/paper/1057326/en

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