In this paper, we consider the efficient numerical scheme for solving time-fractional mobile/immobile transport equation. By utilizing the compact difference operator to approximate the Laplacian, we develop an efficient Crank-Nicolson compact difference scheme based on the modified L1 method. It is proved that the proposed scheme is stable with the accuracy of $ O(\tau^{2-\alpha}+h^4) $, where $ \tau $ and $ h $ are respectively the temporal and spatial stepsizes, and the fractional order $ \alpha\in(0, 1) $. In addition, we improve the computational performance for the non-smooth issue by the fast discrete sine transform technology and the method of adding correction terms. Finally, numerical examples are provided to verify the effectiveness of the proposed scheme.
Citation: Lijuan Nong, An Chen, Qian Yi, Congcong Li. Fast Crank-Nicolson compact difference scheme for the two-dimensional time-fractional mobile/immobile transport equation[J]. AIMS Mathematics, 2021, 6(6): 6242-6254. doi: 10.3934/math.2021366
In this paper, we consider the efficient numerical scheme for solving time-fractional mobile/immobile transport equation. By utilizing the compact difference operator to approximate the Laplacian, we develop an efficient Crank-Nicolson compact difference scheme based on the modified L1 method. It is proved that the proposed scheme is stable with the accuracy of $ O(\tau^{2-\alpha}+h^4) $, where $ \tau $ and $ h $ are respectively the temporal and spatial stepsizes, and the fractional order $ \alpha\in(0, 1) $. In addition, we improve the computational performance for the non-smooth issue by the fast discrete sine transform technology and the method of adding correction terms. Finally, numerical examples are provided to verify the effectiveness of the proposed scheme.
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Lijuan Nong, An Chen, Qian Yi, Congcong Li. Fast Crank-Nicolson compact difference scheme for the two-dimensional time-fractional mobile/immobile transport equation[J]. AIMS Mathematics, 2021, 6(6): 6242-6254. doi: 10.3934/math.2021366
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