In this work, we construct four versions of nonstandard finite difference schemes in order to solve the FitzHugh–Nagumo equation with specified initial and boundary conditions under three different regimes giving rise to three cases. The properties of the methods such as positivity and boundedness are studied. The numerical experiment chosen is quite challenging due to shock‐like profiles. The performance of the four methods is compared by computing L₁, L_∞ errors, rate of convergence with respect to time and central processing unit time at given time, T = 0.5. Error estimates have also been studied for the most efficient scheme.

中文翻译：

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FitzHugh-Nagumo方程的一些非标准有限差分方法的构造和分析

在这项工作中，我们构造了四个版本的非标准有限差分方案，以便在三种不同情况下，在指定的初始和边界条件下求解FitzHugh-Nagumo方程，从而产生三种情况。研究了方法的性质，如正性和有界性。由于具有类似冲击的轮廓，因此选择的数值实验非常具有挑战性。这四种方法的性能是通过计算进行比较大号₁，大号_∞相对于时间和中央处理单元时间在给定的时间，错误，收敛速度Ť  = 0.5。还针对最有效的方案研究了误差估计。