论文标题
完全离散的Fitzhugh-Nagumo类型方程的行驶波解决方案，具有无限范围的相互作用
Travelling wave solutions for fully discrete FitzHugh-Nagumo type equations with infinite-range interactions
论文作者
论文摘要
我们研究了时空离散方案对包括Fitzhugh-Nagumo系统在内的一类反应扩散方程的动力学的影响。对于时间离散化，我们考虑六个向后差分公式（BDF）方法的家族，其中包括众所周知的向后欧拉斯方案。空间离散可以具有无限范围的相互作用，从而使我们可以考虑神经场模型。我们通过将它们视为相应的空间离散系统的奇异扰动，将这些完全离散的系统构建为这些完全离散的系统。特别是，我们为标量完全离散的系统改进了Hupkes和Van Vleck的先前方法，该系统基于Bates，Chen和Chmaj开发的光谱收敛技术。
We investigate the impact of spatial-temporal discretisation schemes on the dynamics of a class of reaction-diffusion equations that includes the FitzHugh-Nagumo system. For the temporal discretisation we consider the family of six backward differential formula (BDF) methods, which includes the well-known backward-Euler scheme. The spatial discretisations can feature infinite-range interactions, allowing us to consider neural field models. We construct travelling wave solutions to these fully discrete systems in the small time-step limit by viewing them as singular perturbations of the corresponding spatially discrete system. In particular, we refine the previous approach by Hupkes and Van Vleck for scalar fully discretised systems, which is based on a spectral convergence technique that was developed by Bates, Chen and Chmaj.
