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Volume 4, Issue 3
Efficient and Stable Numerical Methods for Multi-Term Time Fractional Sub-Diffusion Equations

Jincheng Ren & Zhi-Zhong Sun

DOI: 10.4208/eajam.181113.280514a

East Asian J. Appl. Math., 4 (2014), pp. 242-266.

Published online: 2018-02

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  • Abstract

Some efficient numerical schemes are proposed for solving one-dimensional (1D) and two-dimensional (2D) multi-term time fractional sub-diffusion equations, combining the compact difference approach for the spatial discretisation and $L1$ approximation for the multi-term time Caputo fractional derivatives. The stability and convergence of these difference schemes are theoretically established. Several numerical examples are implemented, testifying to their efficiency and confirming their convergence order.

  • Keywords

Multi-term time fractional sub-diffusion equations, compact/compact ADI difference scheme, discrete energy method, convergence.

  • AMS Subject Headings

65M06, 65M12, 65M15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-4-242, author = {Ren , Jincheng and Sun , Zhi-Zhong}, title = {Efficient and Stable Numerical Methods for Multi-Term Time Fractional Sub-Diffusion Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {4}, number = {3}, pages = {242--266}, abstract = {

Some efficient numerical schemes are proposed for solving one-dimensional (1D) and two-dimensional (2D) multi-term time fractional sub-diffusion equations, combining the compact difference approach for the spatial discretisation and $L1$ approximation for the multi-term time Caputo fractional derivatives. The stability and convergence of these difference schemes are theoretically established. Several numerical examples are implemented, testifying to their efficiency and confirming their convergence order.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.181113.280514a}, url = {http://global-sci.org/intro/article_detail/eajam/10835.html} }
TY - JOUR T1 - Efficient and Stable Numerical Methods for Multi-Term Time Fractional Sub-Diffusion Equations AU - Ren , Jincheng AU - Sun , Zhi-Zhong JO - East Asian Journal on Applied Mathematics VL - 3 SP - 242 EP - 266 PY - 2018 DA - 2018/02 SN - 4 DO - http://doi.org/10.4208/eajam.181113.280514a UR - https://global-sci.org/intro/article_detail/eajam/10835.html KW - Multi-term time fractional sub-diffusion equations, compact/compact ADI difference scheme, discrete energy method, convergence. AB -

Some efficient numerical schemes are proposed for solving one-dimensional (1D) and two-dimensional (2D) multi-term time fractional sub-diffusion equations, combining the compact difference approach for the spatial discretisation and $L1$ approximation for the multi-term time Caputo fractional derivatives. The stability and convergence of these difference schemes are theoretically established. Several numerical examples are implemented, testifying to their efficiency and confirming their convergence order.

Ren , Jincheng and Sun , Zhi-Zhong. (2018). Efficient and Stable Numerical Methods for Multi-Term Time Fractional Sub-Diffusion Equations. East Asian Journal on Applied Mathematics. 4 (3). 242-266. doi:10.4208/eajam.181113.280514a
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