Year: 2022
Author: Shuiping Yang, Yubin Liu, Hongyu Liu, Chao Wang
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 1 : pp. 56–78
Abstract
In this paper, we consider the numerical solutions of the semilinear Riesz space-fractional diffusion equations (RSFDEs) with time delay, which constitute an important class of differential equations of practical significance. We develop a novel implicit alternating direction method that can effectively and efficiently tackle the RSFDEs in both two and three dimensions. The numerical method is proved to be uniquely solvable, stable and convergent with second order accuracy in both space and time. Numerical results are presented to verify the accuracy and efficiency of the proposed numerical scheme.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2020-0387
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 1 : pp. 56–78
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Semilinear Riesz space fractional diffusion equations with time delay implicit alternating direction method stability and convergence.