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Volume 11, Issue 4
A Fast Temporal Second-Order Compact ADI Scheme for Time Fractional Mixed Diffusion-Wave Equations

Rui-Lian Du & Zhi-Zhong Sun

East Asian J. Appl. Math., 11 (2021), pp. 647-673.

Published online: 2021-08

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  • Abstract

A fast temporal second-order compact alternating direction implicit (ADI) difference scheme is proposed and analysed for 2D time fractional mixed diffusion-wave equations. The time fractional operators are approximated by mixed fast $L2$-$1_σ$ and fast $L1$-type formulas derived by using the sum-of-exponentials technique. The spatial derivatives are approximated by the fourth-order compact difference operator, which can be implemented by an ADI approach with relatively low computational cost. The resulting fast algorithm is computationally efficient in long-time simulations since the computational cost is significantly reduced. Numerical experiments confirm the effectiveness of the algorithm and theoretical analysis.

  • AMS Subject Headings

65M06, 65M12, 65M15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-11-647, author = {Du , Rui-Lian and Sun , Zhi-Zhong}, title = {A Fast Temporal Second-Order Compact ADI Scheme for Time Fractional Mixed Diffusion-Wave Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2021}, volume = {11}, number = {4}, pages = {647--673}, abstract = {

A fast temporal second-order compact alternating direction implicit (ADI) difference scheme is proposed and analysed for 2D time fractional mixed diffusion-wave equations. The time fractional operators are approximated by mixed fast $L2$-$1_σ$ and fast $L1$-type formulas derived by using the sum-of-exponentials technique. The spatial derivatives are approximated by the fourth-order compact difference operator, which can be implemented by an ADI approach with relatively low computational cost. The resulting fast algorithm is computationally efficient in long-time simulations since the computational cost is significantly reduced. Numerical experiments confirm the effectiveness of the algorithm and theoretical analysis.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.271220.090121}, url = {http://global-sci.org/intro/article_detail/eajam/19366.html} }
TY - JOUR T1 - A Fast Temporal Second-Order Compact ADI Scheme for Time Fractional Mixed Diffusion-Wave Equations AU - Du , Rui-Lian AU - Sun , Zhi-Zhong JO - East Asian Journal on Applied Mathematics VL - 4 SP - 647 EP - 673 PY - 2021 DA - 2021/08 SN - 11 DO - http://doi.org/10.4208/eajam.271220.090121 UR - https://global-sci.org/intro/article_detail/eajam/19366.html KW - Time fractional mixed diffusion-wave equations, SOEs technique, ADI difference scheme, stability, convergence. AB -

A fast temporal second-order compact alternating direction implicit (ADI) difference scheme is proposed and analysed for 2D time fractional mixed diffusion-wave equations. The time fractional operators are approximated by mixed fast $L2$-$1_σ$ and fast $L1$-type formulas derived by using the sum-of-exponentials technique. The spatial derivatives are approximated by the fourth-order compact difference operator, which can be implemented by an ADI approach with relatively low computational cost. The resulting fast algorithm is computationally efficient in long-time simulations since the computational cost is significantly reduced. Numerical experiments confirm the effectiveness of the algorithm and theoretical analysis.

Du , Rui-Lian and Sun , Zhi-Zhong. (2021). A Fast Temporal Second-Order Compact ADI Scheme for Time Fractional Mixed Diffusion-Wave Equations. East Asian Journal on Applied Mathematics. 11 (4). 647-673. doi:10.4208/eajam.271220.090121
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