Volume 9, Issue 4
A Second-Order Accurate Implicit Difference Scheme for Time Fractional Reaction-Diffusion Equation with Variable Coefficients and Time Drift Term

Yong-Liang Zhao, Pei-Yong Zhu, Xian-Ming Gu & Xi-Le Zhao

East Asian J. Appl. Math., 9 (2019), pp. 723-754.

Published online: 2019-10

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  • Abstract

Two implicit finite difference schemes combined with the Alikhanov’s L2-1σformula are applied to one- and two-dimensional time fractional reaction-diffusion equations with variable coefficients and time drift term. The unconditional stability and L2 - convergence of the methods are established. It is shown that the convergence order of the methods is equal to 2 both in time and space. Numerical experiments confirm the theoretical results. Moreover, since the arising linear systems can be ill-conditioned, three preconditioned iterative methods are employed.

  • Keywords

Caputo fractional derivative, L2-1σ-formula, finite difference scheme, time fractional reaction-diffusion equation, iterative method.

  • AMS Subject Headings

65M06, 65M12, 65N06

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

uestc_ylzhao@sina.com (Yong-Liang Zhao)

zpy6940@uestc.edu.cn (Pei-Yong Zhu)

guxianming@live.cn (Xian-Ming Gu)

xlzhao122003@163.com (Xi-Le Zhao)

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@Article{EAJAM-9-723, author = {Zhao , Yong-Liang and Zhu , Pei-Yong and Gu , Xian-Ming and Zhao , Xi-Le }, title = {A Second-Order Accurate Implicit Difference Scheme for Time Fractional Reaction-Diffusion Equation with Variable Coefficients and Time Drift Term}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {4}, pages = {723--754}, abstract = {

Two implicit finite difference schemes combined with the Alikhanov’s L2-1σformula are applied to one- and two-dimensional time fractional reaction-diffusion equations with variable coefficients and time drift term. The unconditional stability and L2 - convergence of the methods are established. It is shown that the convergence order of the methods is equal to 2 both in time and space. Numerical experiments confirm the theoretical results. Moreover, since the arising linear systems can be ill-conditioned, three preconditioned iterative methods are employed.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.200618.250319}, url = {http://global-sci.org/intro/article_detail/eajam/13330.html} }
TY - JOUR T1 - A Second-Order Accurate Implicit Difference Scheme for Time Fractional Reaction-Diffusion Equation with Variable Coefficients and Time Drift Term AU - Zhao , Yong-Liang AU - Zhu , Pei-Yong AU - Gu , Xian-Ming AU - Zhao , Xi-Le JO - East Asian Journal on Applied Mathematics VL - 4 SP - 723 EP - 754 PY - 2019 DA - 2019/10 SN - 9 DO - http://dor.org/10.4208/eajam.200618.250319 UR - https://global-sci.org/intro/eajam/13330.html KW - Caputo fractional derivative, L2-1σ-formula, finite difference scheme, time fractional reaction-diffusion equation, iterative method. AB -

Two implicit finite difference schemes combined with the Alikhanov’s L2-1σformula are applied to one- and two-dimensional time fractional reaction-diffusion equations with variable coefficients and time drift term. The unconditional stability and L2 - convergence of the methods are established. It is shown that the convergence order of the methods is equal to 2 both in time and space. Numerical experiments confirm the theoretical results. Moreover, since the arising linear systems can be ill-conditioned, three preconditioned iterative methods are employed.

Yong-Liang Zhao, Pei-Yong Zhu, Xian-Ming Gu & Xi-Le Zhao. (2019). A Second-Order Accurate Implicit Difference Scheme for Time Fractional Reaction-Diffusion Equation with Variable Coefficients and Time Drift Term. East Asian Journal on Applied Mathematics. 9 (4). 723-754. doi:10.4208/eajam.200618.250319
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