%0 Journal Article
%T Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation
%J Computational Methods for Differential Equations
%I University of Tabriz
%Z 2345-3982
%A Abdollahy, Zeynab
%A Mahmoudi, Yaghoub
%A Salimi shamloo, Ali
%A Baghmisheh, Mahdi
%D 2022
%\ 07/01/2022
%V 10
%N 3
%P 799-815
%! Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation
%K Fractional derivatives
%K Fractional diffusion equation
%K Riesz fractional derivative
%K Finite differences
%R 10.22034/cmde.2021.45950.1927
%X 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 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.
%U https://cmde.tabrizu.ac.ir/article_13735_61416bbb597edb9b6d5f95d2ce68648f.pdf