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Volume 14, Issue 1
Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay

Shuiping Yang, Yubin Liu, Hongyu Liu & Chao Wang

DOI: 10.4208/aamm.OA-2020-0387

Adv. Appl. Math. Mech., 14 (2022), pp. 56-78.

Published online: 2021-11

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  • 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.

  • Keywords

Semilinear Riesz space fractional diffusion equations with time delay, implicit alternating direction method, stability and convergence.

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-14-56, author = {Yang , ShuipingLiu , YubinLiu , Hongyu and Wang , Chao}, title = {Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2021}, volume = {14}, number = {1}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0387}, url = {http://global-sci.org/intro/article_detail/aamm/19976.html} }
TY - JOUR T1 - Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay AU - Yang , Shuiping AU - Liu , Yubin AU - Liu , Hongyu AU - Wang , Chao JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 56 EP - 78 PY - 2021 DA - 2021/11 SN - 14 DO - http://doi.org/10.4208/aamm.OA-2020-0387 UR - https://global-sci.org/intro/article_detail/aamm/19976.html KW - Semilinear Riesz space fractional diffusion equations with time delay, implicit alternating direction method, stability and convergence. AB -

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.

Yang , ShuipingLiu , YubinLiu , Hongyu and Wang , Chao. (2021). Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay. Advances in Applied Mathematics and Mechanics. 14 (1). 56-78. doi:10.4208/aamm.OA-2020-0387
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