An explicit nonstandard finite difference scheme for the FitzHugh–Nagumo equations
An explicit nonstandard finite difference scheme for the FitzHugh–Nagumo equations
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DOI：
10.1080/00207160.2018.1546849
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发表时间：
2018-11
影响因子：
1.8
通讯作者：
M. Chapwanya;O. A. Jejeniwa;A. Appadu;J. Lubuma
中科院分区：
文献类型：
--
作者：
M. Chapwanya;O. A. Jejeniwa;A. Appadu;J. Lubuma
In this work, we consider numerical solutions of the FitzHugh–Nagumo system of equations describing the propagation of electrical signals in nerve axons. The system consists of two coupled equations: a nonlinear partial differential equation and a linear ordinary differential equation. We begin with a review of the qualitative properties of the nonlinear space independent system of equations. The subequation approach is applied to derive dynamically consistent schemes for the submodels. This is followed by a consistent and systematic merging of the subschemes to give three explicit nonstandard finite difference schemes in the limit of fast extinction and slow recovery. A qualitative study of the schemes together with the error analysis is presented. Numerical simulations are given to support the theoretical results and verify the efficiency of the proposed schemes.
