In this paper, we present a numerical strategy to check the strong stability (or GKS-stability) of one-step explicit finite difference schemes for the one-dimensional advection equation with an inflow boundary condition. The strong stability is studied using the Kreiss-Lopatinskii theory. We introduce a new tool, the intrinsic Kreiss-Lopatinskii determinant, which possesses the same regularity as the vector bundle of discrete stable solutions. By applying standard results of complex analysis to this determinant, we are able to relate the strong stability of numerical schemes to the computation of a winding number, which is robust and cheap. The study is illustrated with the O3 scheme and the fifth-order Lax-Wendroff (LW5) scheme together with a reconstruction procedure at the boundary.

翻译：本文提出了一种数值策略，用于检验一维对流方程在流入边界条件下单步显式有限差分格式的强稳定性（或称GKS稳定性）。该强稳定性研究基于Kreiss-Lopatinskii理论。我们引入了一个新工具——内禀Kreiss-Lopatinskii行列式，其正则性与离散稳定解的向量丛相同。通过将复分析的标准结果应用于该行列式，我们能够将数值格式的强稳定性与绕数计算相关联，该方法既稳健又廉价。该研究以O3格式和五阶Lax-Wendroff（LW5）格式结合边界重构过程为例进行了说明。