A novel compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction–diffusion equations

Abstract

This paper is concerned with the construction and analysis of a novel linearized compact ADI scheme for the two-dimensional Riesz space fractional nonlinear reaction–diffusion equations. Convergence of the proposed scheme is proved. The highlight is that the time discretization is achieved by applying a second-order, one-step and linearized method. The time discretization requires only one starting value, which is sharp contrast to the extrapolated Crank–Nicolson method or the usual second-order linearized schemes. Numerical examples on several fractional models are presented to confirm our theoretical results.