In this paper, with the help of a computer package program, the auto-Bäcklund transformation method (aBTM) and the finite forward difference method are used for obtaining the wave solutions and the numeric and exact approximations to the FitzHugh–Nagumo (F-N) equation, respectively. We successfully obtain some wave solutions to this equation by using aBTM. We then employ the finite difference method (FDM) in approximating the exact and numerical solutions to this equation by taking one of the obtained wave solutions into consideration. We also present the comparison between exact and numeric approximations and support the comparison with a graphic plot. Moreover, the Fourier von-Neumann stability analysis is used in checking the stability of the numeric scheme. We also present the [Formula: see text] and [Formula: see text] error norms of the solutions to this equation.

中文翻译：

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关于 FitzHugh-Nagumo 方程的精确和数值解

在本文中，在计算机程序包的帮助下，使用自动 Bäcklund 变换方法 (aBTM) 和有限前向差分法来获得波解以及 FitzHugh-Nagumo (FN) 方程的数值和精确逼近， 分别。我们通过使用 aBTM 成功地获得了该方程的一些波动解。然后，我们采用有限差分法 (FDM) 通过考虑获得的波解之一来逼近该方程的精确和数值解。我们还提供了精确近似值和数值近似值之间的比较，并支持用图形进行比较。此外，傅里叶冯诺依曼稳定性分析用于检查数值方案的稳定性。我们还介绍了 [公式：见正文] 和 [公式：