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

Weiping Bu, Yifa Tang, Yingchuan Wu and Jiye Yang

Applied Mathematics and Computation, 2015, vol. 257, issue C, 355-364

Abstract: 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.

Keywords: Alternating direction implicit method; Galerkin finite element method; Fractional FitzHugh–Nagumo monodomain model; Fractional reaction diffusion equation (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:257:y:2015:i:c:p:355-364

DOI: 10.1016/j.amc.2014.09.034

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