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Volume 38, Issue 3
A Fully Discrete Implicit-Explicit Finite Element Method for Solving the FitzHugh-Nagumo Model

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

DOI: 10.4208/jcm.1901-m2017-0263

J. Comp. Math., 38 (2020), pp. 469-486.

Published online: 2020-03

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65M12, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

caili@nwpu.edu.cn (Li Cai)

sunye@mail.nwpu.edu.cn (Ye Sun)

ffjing@nwpu.edu.cn (Feifei Jing)

liyiqiang@mail.nwpu.edu.cn (Yiqiang Li)

xqshen@xaut.edu.cn (Xiaoqin Shen)

yfnie@nwpu.edu.cn (Yufeng Nie)

  • BibTex
  • RIS
  • TXT
@Article{JCM-38-469, author = {Cai , LiSun , YeJing , FeifeiLi , YiqiangShen , Xiaoqin and Nie , Yufeng}, title = {A Fully Discrete Implicit-Explicit Finite Element Method for Solving the FitzHugh-Nagumo Model}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {3}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1901-m2017-0263}, url = {http://global-sci.org/intro/article_detail/jcm/15796.html} }
TY - JOUR T1 - A Fully Discrete Implicit-Explicit Finite Element Method for Solving the FitzHugh-Nagumo Model AU - Cai , Li AU - Sun , Ye AU - Jing , Feifei AU - Li , Yiqiang AU - Shen , Xiaoqin AU - Nie , Yufeng JO - Journal of Computational Mathematics VL - 3 SP - 469 EP - 486 PY - 2020 DA - 2020/03 SN - 38 DO - http://doi.org/10.4208/jcm.1901-m2017-0263 UR - https://global-sci.org/intro/article_detail/jcm/15796.html KW - Finite element method, nonlinear reaction term, FitzHugh-Nagumo model, implicit-explicit scheme, stability and error estimates. AB -

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.

Cai , LiSun , YeJing , FeifeiLi , YiqiangShen , Xiaoqin and Nie , Yufeng. (2020). A Fully Discrete Implicit-Explicit Finite Element Method for Solving the FitzHugh-Nagumo Model. Journal of Computational Mathematics. 38 (3). 469-486. doi:10.4208/jcm.1901-m2017-0263
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