A fourth-order compact ADI scheme for solving a two-dimensional time-fractional reaction-subdiffusion equation

This article aims at developing a computational scheme for solving the time fractional reaction-subdiffusion (TFRSD) equation in two space dimensions. The Caputo fractional derivative is used to describe the time-fractional derivative appearing in the problem and it is approximated by using the L1 scheme. A compact difference scheme of order four is utilized for discretization of the spatial derivatives. Some test problems are solved to investigate the accuracy of the scheme. The computed results confirm that the scheme has convergence of order four in space and an order of \({\min {\{2-\alpha ,1+\alpha \}}}\) $min\{2-\alpha ,1+\alpha \}$ in the time direction, where \(\alpha \in (0,1)\) $\alpha \in (0,1)$ is the order of fractional derivative. Moreover, the computed results are compared with those obtained by other methods in order to justify the advantage of proposed algorithm.