Numerical simulation for the two-dimensional and three-dimensional Riesz space fractional diffusion equations with delay and a nonlinear reaction term

Abstract

ABSTRACTIn this research, we consider the alternating direction implicit method for solving the two-dimensional and three-dimensional Riesz space fractional diffusion equations with delay and a nonlinear reaction term. The corresponding theoretical results including stability and convergence are provided. Moreover, the convergence order of the proposed method is improved by using the Richardson extrapolation method. The numerical results are presented to show the robustness and effectiveness of the numerical method.