A Fully Discrete Implicit-Explicit Finite Element Method for Solving the FitzHugh-Nagumo Model

A Fully Discrete Implicit-Explicit Finite Element Method for Solving the FitzHugh-Nagumo Model

Year:    2020

Author:    Li Cai, Ye Sun, Feifei Jing, Yiqiang Li, Xiaoqin Shen, Yufeng Nie

Journal of Computational Mathematics, Vol. 38 (2020), Iss. 3 : pp. 469–486

Abstract

This work develops a fully discrete implicit-explicit finite element scheme for a parabolic-ordinary system with a nonlinear reaction term which is known as the FitzHugh-Nagumo model from physiology. The first-order backward Euler discretization for the time derivative, and an implicit-explicit discretization for the nonlinear reaction term are employed for the model, with a simple linearization technique used to make the process of solving equations more efficient. The stability and convergence of the fully discrete implicit-explicit finite element method are proved, which shows that the FitzHugh-Nagumo model is accurately solved and the trajectory of potential transmission is obtained. The numerical results are also reported to verify the convergence results and the stability of the proposed method.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1901-m2017-0263

Journal of Computational Mathematics, Vol. 38 (2020), Iss. 3 : pp. 469–486

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Finite element method nonlinear reaction term FitzHugh-Nagumo model implicit-explicit scheme stability and error estimates.

Author Details

Li Cai

Ye Sun

Feifei Jing

Yiqiang Li

Xiaoqin Shen

Yufeng Nie

  1. A fast time integral finite difference method for a space-time fractional FitzHugh-Nagumo monodomain model in irregular domains

    Cai, Li | Cao, Jin | Jing, Feifei | Wang, Yongheng

    Journal of Computational Physics, Vol. 501 (2024), Iss. P.112744

    https://doi.org/10.1016/j.jcp.2023.112744 [Citations: 2]
  2. Simulation of action potential propagation based on the ghost structure method

    Wang, Yongheng | Cai, Li | Luo, Xiaoyu | Ying, Wenjun | Gao, Hao

    Scientific Reports, Vol. 9 (2019), Iss. 1

    https://doi.org/10.1038/s41598-019-47321-2 [Citations: 3]
  3. Spiral-generation mechanism in the two-dimensional FitzHugh-Nagumo system

    Rubio-Mercedes, C. E. | Lozada-Cruz, G. | Gallego, F. Ortegón

    Ricerche di Matematica, Vol. 73 (2024), Iss. 5 P.2849

    https://doi.org/10.1007/s11587-022-00725-1 [Citations: 0]