Crank–Nicolson ADI Galerkin finite element method for two-dimensional fractional FitzHugh–Nagumo monodomain model

摘要

In this paper, a two-dimensional fractional FitzHugh–Nagumo monodomain model (2D-FFHNMM) with zero Dirichlet boundary condition is considered. The model consists of a coupled two-dimensional space fractional nonlinear reaction–diffusion model (2D-SFNRDM) and an ordinary differential equation. The 2D-SFNRDM and ordinary differential equation are decoupled at each time step. A new Crank–Nicolson alternating direction implicit (ADI) Galerkin finite element method for the 2D-SFNRDM is developed. The stability and convergence of the numerical method are discussed. Finally, some numerical examples on 2D-SFNRDM and 2D-FFHNMM are given for verification of our theoretical analysis.