Abstract In this work, we discuss the stability and convergence of the Fourier pseudo-spectral scheme coupled with several linearized finite difference methods for FitzHugh-Nagumo model. The work of this article has three main features. Firstly, our full-discrete schemes are linear and easy to implement for two dimensional or three dimensional simulations. Secondly, by constructing the auxiliary interpolation equation, the L ∞ uniform boundedness and the error estimate of the numerical solutions are obtained. Finally, the most important is that our numerical schemes are stable provided only time and space steps are bounded by two constants respectively. It is worth mentioning that this kind of stability restriction is very weak, it does not require any scaling law between time step and space size. Numerical examples are presented to verify validity of the proposed scheme.

中文翻译：

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FitzHugh-Nagumo模型傅里叶伪谱方法的稳定性和收敛性分析

摘要 在这项工作中，我们讨论了 FitzHugh-Nagumo 模型的傅立叶伪谱方案与几种线性化有限差分方法相结合的稳定性和收敛性。本文的工作具有三个主要特点。首先，我们的全离散方案是线性的，易于实现二维或三维模拟。其次，通过构造辅助插值方程，得到了数值解的L ∞ 一致有界和误差估计。最后，最重要的是我们的数值方案是稳定的，只要时间和空间步长分别受两个常数的限制。值得一提的是，这种稳定性限制非常弱，它不需要任何时间步长和空间大小之间的标度律。