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Volume 8, Issue 4
A Fourth Order Finite Difference Method for Time-Space Fractional Diffusion Equations

Sadia Arshad, Dumitru Baleanu, Jianfei Huang, Yifa Tang & Yue Zhao

East Asian J. Appl. Math., 8 (2018), pp. 764-781.

Published online: 2018-10

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  • Abstract

A finite difference method for a class of time-space fractional diffusion equations is considered. The trapezoidal formula and a fourth-order fractional compact difference scheme are, respectively, used in temporal and spatial discretisations and the method stability is studied. Theoretical estimates of the convergence in the $L_2$ -norm are shown to be $\mathscr{O}(τ^2+h^4)$, where $τ$ and $h$ are time and space mesh sizes. Numerical examples confirm theoretical results.

  • AMS Subject Headings

65M06, 65M12, 35R11

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-8-764, author = {Sadia Arshad, Dumitru Baleanu, Jianfei Huang, Yifa Tang and Yue Zhao}, title = {A Fourth Order Finite Difference Method for Time-Space Fractional Diffusion Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {8}, number = {4}, pages = {764--781}, abstract = {

A finite difference method for a class of time-space fractional diffusion equations is considered. The trapezoidal formula and a fourth-order fractional compact difference scheme are, respectively, used in temporal and spatial discretisations and the method stability is studied. Theoretical estimates of the convergence in the $L_2$ -norm are shown to be $\mathscr{O}(τ^2+h^4)$, where $τ$ and $h$ are time and space mesh sizes. Numerical examples confirm theoretical results.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.280218.210518}, url = {http://global-sci.org/intro/article_detail/eajam/12818.html} }
TY - JOUR T1 - A Fourth Order Finite Difference Method for Time-Space Fractional Diffusion Equations AU - Sadia Arshad, Dumitru Baleanu, Jianfei Huang, Yifa Tang & Yue Zhao JO - East Asian Journal on Applied Mathematics VL - 4 SP - 764 EP - 781 PY - 2018 DA - 2018/10 SN - 8 DO - http://doi.org/10.4208/eajam.280218.210518 UR - https://global-sci.org/intro/article_detail/eajam/12818.html KW - Fractional diffusion equation, Riesz derivative, high-order approximation, stability, convergence. AB -

A finite difference method for a class of time-space fractional diffusion equations is considered. The trapezoidal formula and a fourth-order fractional compact difference scheme are, respectively, used in temporal and spatial discretisations and the method stability is studied. Theoretical estimates of the convergence in the $L_2$ -norm are shown to be $\mathscr{O}(τ^2+h^4)$, where $τ$ and $h$ are time and space mesh sizes. Numerical examples confirm theoretical results.

Sadia Arshad, Dumitru Baleanu, Jianfei Huang, Yifa Tang and Yue Zhao. (2018). A Fourth Order Finite Difference Method for Time-Space Fractional Diffusion Equations. East Asian Journal on Applied Mathematics. 8 (4). 764-781. doi:10.4208/eajam.280218.210518
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