Finite Difference Approximations for Fractional Reaction-Diffusion Equations and the Application in PM2.5

Abstract

In this paper, fractional reaction-diffusion equations are used to model the diffusion of PM2.5 in the air. First, based on the shifted Grünwald formula, we propose the fractional Crank-Nicolson method to solve the fractional reaction-diffusion equations. Then we prove the existence and uniqueness of numerical solutions, and establish the stability and convergence of the method. Furthermore, numerical examples are also provided to show the efficiency of the method. Finally, the diffusion of PM2.5 in Guangzhou is simulated by using this method under appropriate parameters .