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

Stability of finite difference schemes for the hyperbolic initial boundary value problem by winding number computations