Counterexamples to a stability barrier (Q1825010)

The authors study the highest possible order of stable multistep difference schemes for the linear constant coefficient advection equation. Previously \textit{G. Strang} and \textit{A. Iserles} [SIAM J. Numer. Anal. 20, 1251-1257 (1983; Zbl 0529.65058)] have given a barrier for the order of stable schemes which is independent of the order of time levels. It is shown that the barrier in question can be improved for special schemes and it is conjectured that a correct barrier should be that the order p is bounded by \(p\leq 2\) min(r,s), where r,s are the numbers of downwind and upwind points, respectively. This conjecture is supported by numerical evidence.