Compact implicit integration factor method for two-dimensional space-fractional advection-diffusion-reaction equations

Abstract

In this paper, we intend to develop an effective numerical method to solve a class of two-dimensional space-fractional advection-diffusion-reaction equations. After spatially discretizing this equation using the fractional centered difference formula, it leads to a system of nonlinear ordinary differential equations. The compact implicit integration factor method is applied to solve the resulting system to achieve good stability and robustness. Linear stability analysis and numerical experiments are given to verify that the compact implicit integration factor method has excellent efficiency and stability properties.