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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