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

在本文中，我们提出了一种稳定的有限差分方法来解决二维域中的分数反应扩散系统。空间离散化是通过加权偏移 Grünwald 差分 (WSGD) 实现的，这导致非线性常微分方程 (ODE) 的刚性系统。该常微分方程组通过高效的紧凑隐式积分因子 (cIIF) 方法求解。二阶 cIIF 方案的稳定性在离散\(L^{2}\) -范数中得到证明。我们还证明了所提出方案的二阶收敛性。给出了数值例子来证明该方法的准确性、效率和稳健性。