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Abdollahy, Zeynab, Mahmoudi, Yaghoub, Salimi shamloo, Ali, Baghmisheh, Mahdi. (1401). Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation. سامانه مدیریت نشریات علمی, 10(3), 799-815. doi: 10.22034/cmde.2021.45950.1927
Zeynab Abdollahy; Yaghoub Mahmoudi; Ali Salimi shamloo; Mahdi Baghmisheh. "Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation". سامانه مدیریت نشریات علمی, 10, 3, 1401, 799-815. doi: 10.22034/cmde.2021.45950.1927
Abdollahy, Zeynab, Mahmoudi, Yaghoub, Salimi shamloo, Ali, Baghmisheh, Mahdi. (1401). 'Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation', سامانه مدیریت نشریات علمی, 10(3), pp. 799-815. doi: 10.22034/cmde.2021.45950.1927
Abdollahy, Zeynab, Mahmoudi, Yaghoub, Salimi shamloo, Ali, Baghmisheh, Mahdi. Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation. سامانه مدیریت نشریات علمی, 1401; 10(3): 799-815. doi: 10.22034/cmde.2021.45950.1927

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

Computational Methods for Differential Equations
مقاله 18، دوره 10، شماره 3، مهر 2022، صفحه 799-815    اصل مقاله (3.4 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.45950.1927
نویسندگان
Zeynab Abdollahy1؛ Yaghoub Mahmoudi* 1؛ Ali Salimi shamloo2؛ Mahdi Baghmisheh1
1Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran.
2Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran.
چکیده
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.
کلیدواژه‌ها
Fractional derivatives؛ Fractional diffusion equation؛ Riesz fractional derivative؛ Finite differences
مراجع
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