An ADI compact difference scheme for the two-dimensional semilinear time-fractional mobile–immobile equation

被引：0
作者：
Huifa Jiang
Da Xu
Wenlin Qiu
Jun Zhou
机构：
[1] Hunan Normal University,Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics
来源：
Computational and Applied Mathematics | 2020年 / 39卷
关键词：
Semilinear time-fractional mobile–immobile equations; ADI compact difference scheme; Stability; Convergence; Numerical experiments; 35M13; 65M06; 65M12;
D O I：
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学科分类号：
摘要：
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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