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Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay

Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay
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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.

Author Details

Shuiping Yang

Yubin Liu

Hongyu Liu

Chao Wang

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