Stable finite difference method for fractional reaction–diffusion equations by compact implicit integration factor methods

Abstract In this paper we propose a stable finite difference method to solve the fractional reaction–diffusion systems in two-dimensional domain. The space discretization is implemented by weighted shifted Grünwald (WSGD) which results stiff system of nonlinear ordinary differential equations (ODEs). This solved an efficient compact implicit integration factor (cIIF) method. stability second order cIIF scheme proved discrete $L^{2}$ L 2 -norm. We also prove second-order convergence proposed scheme. Numerical examples are given demonstrate accuracy, efficiency, and robustness