University of TabrizComputational Methods for Differential Equations2345-398210320220701Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation7998151373510.22034/cmde.2021.45950.1927ENZeynabAbdollahyDepartment of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran.YaghoubMahmoudiDepartment of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran.AliSalimi ShamlooDepartment of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran.MahdiBaghmishehDepartment of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran.Journal Article20210508In 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 GrÂ¨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