TY - JOUR
ID - 13735
TI - Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Abdollahy, Zeynab
AU - Mahmoudi, Yaghoub
AU - Salimi shamloo, Ali
AU - Baghmisheh, Mahdi
AD - Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran.
AD - Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran.
Y1 - 2022
PY - 2022
VL - 10
IS - 3
SP - 799
EP - 815
KW - Fractional derivatives
KW - Fractional diffusion equation
KW - Riesz fractional derivative
KW - Finite differences
DO - 10.22034/cmde.2021.45950.1927
N2 - 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.
UR - https://cmde.tabrizu.ac.ir/article_13735.html
L1 - https://cmde.tabrizu.ac.ir/article_13735_61416bbb597edb9b6d5f95d2ce68648f.pdf
ER -