A Second-Order Accurate Implicit Difference Scheme for Time Fractional Reaction-Diffusion Equation with Variable Coefficients and Time Drift Term

Abstract

Two implicit finite difference schemes combined with the Alikhanov's $L$2-1$σ$-formula are applied to one- and two-dimensional time fractional reaction-diffusion equations with variable coefficients and time drift term. The unconditional stability and $L$2-convergence of the methods are established. It is shown that the convergence order of the methods is equal to 2 both in time and space. Numerical experiments confirm the theoretical results. Moreover, since the arising linear systems can be ill-conditioned, three preconditioned iterative methods are employed.