A FULLY DISCRETE IMPLICIT-EXPLICIT FINITE ELEMENT METHOD FOR SOLVING THE FITZHUGH-NAGUMO MODEL

• 来源期刊: 计算数学（英文版）
• 关键词: Finite element method Nonlinear reaction term FitzHugh-Nagumo model Implicit-explicit scheme Stability and error estimates
• 年，卷（期）: 2020,（3）
• 页码范围: 469-486
• 页数: 18页
• 语种: 英文
• DOI: 10.4208/jcm.1901-m2017-0263

摘要

This work develops a fully discrete implicit-explicit finite element scheme for a parabolicordinary 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.