论文标题
Fitzhugh-Nagumo运输方程的渐近保存方案具有强烈的局部相互作用
Asymptotic preserving schemes for the FitzHugh-Nagumo transport equation with strong local interactions
论文作者
论文摘要
本文致力于基于粒子方法的强烈局部相互作用的空间扩展的Fitzhugh-Nagumo传输方程的数值近似。在此制度中，时间步长可以受到与交互内核相关的稳定性约束。为了避免这种限制，我们的方法基于高阶隐式数字方案。因此，当相互作用的大小变大时，该方法提供了宏观反应 - 扩散菲茨胡格 - 纳古莫系统的一致离散化。我们执行一些理论上的证据，并执行几个数值实验，以对该方法及其基本概念建立可靠的验证。
This paper is devoted to the numerical approximation of the spatially-extended FitzHugh-Nagumo transport equation with strong local interactions based on a particle method. In this regime, the time step can be subject to stability constraints related to the interaction kernel. To avoid this limitation, our approach is based on higher-order implicit-explicit numerical schemes. Thus, when the magnitude of the interactions becomes large, this method provides a consistent discretization of the macroscopic reaction-diffusion FitzHugh-Nagumo system. We carry out some theoretical proofs and perform several numerical experiments that establish a solid validation of the method and its underlying concepts.
