University of Tabriz Computational Methods for Differential Equations 2345-3982 10 3 2022 07 01 Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation 799 815 13735 10.22034/cmde.2021.45950.1927 EN Zeynab Abdollahy Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran. Yaghoub Mahmoudi Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran. Ali Salimi Shamloo Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran. Mahdi Baghmisheh Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran. Journal Article 2021 05 08 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. https://cmde.tabrizu.ac.ir/article_13735_61416bbb597edb9b6d5f95d2ce68648f.pdf