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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Abdollahy, Z., Mahmoudi, Y., Salimi shamloo, A., Baghmisheh, M. (2022). Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation. Computational Methods for Differential Equations, 10(3), 799-815. doi: 10.22034/cmde.2021.45950.1927
MLA
Zeynab Abdollahy; Yaghoub Mahmoudi; Ali Salimi shamloo; Mahdi Baghmisheh. "Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation". Computational Methods for Differential Equations, 10, 3, 2022, 799-815. doi: 10.22034/cmde.2021.45950.1927
HARVARD
Abdollahy, Z., Mahmoudi, Y., Salimi shamloo, A., Baghmisheh, M. (2022). 'Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation', Computational Methods for Differential Equations, 10(3), pp. 799-815. doi: 10.22034/cmde.2021.45950.1927
VANCOUVER
Abdollahy, Z., Mahmoudi, Y., Salimi shamloo, A., Baghmisheh, M. Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation. Computational Methods for Differential Equations, 2022; 10(3): 799-815. doi: 10.22034/cmde.2021.45950.1927