Abstract
In this paper, an alternating direction implicit (ADI) compact difference scheme will be proposed for solving semilinear time-fractional mobile–immobile equations in two dimensions. In the time direction, the first derivative and Caputo derivative term are treated by means of second-order backward differentiation formula (BDF) and L1 discrete method, respectively. Then, the nonlinear term is linearized and a fully discrete ADI compact difference scheme is constructed with the space discretization by the fourth-order compact approximation. The stability and convergence are established by the discrete energy method. In addition, the accuracy and effectiveness of the scheme are illustrated by several numerical experiments.
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Acknowledgements
The project was supported by the National Natural Science Foundation of China (No. 12071127) and the Construct Program of the Key Discipline in Hunan Province, Performance Computing and Stochastic Information Processing (Ministry of Education of China).
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Communicated by José Tenreiro Machado.
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Jiang, H., Xu, D., Qiu, W. et al. An ADI compact difference scheme for the two-dimensional semilinear time-fractional mobile–immobile equation. Comp. Appl. Math. 39, 287 (2020). https://doi.org/10.1007/s40314-020-01345-x
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DOI: https://doi.org/10.1007/s40314-020-01345-x
Keywords
- Semilinear time-fractional mobile–immobile equations
- ADI compact difference scheme
- Stability
- Convergence
- Numerical experiments