A proof of the order barrier for upwind schemes by Dahlquist's second barrier (Q1077138)

\textit{B. Engquist} and \textit{S. Osher} [Math. Comput. 36, 321-351 (1981; Zbl 0469.65067)] have shown that stable semi-discretizations of \(u_ t=u_ x\) cannot have an order exceeding two. This paper gives new insight into the relations between this result and the second Dahlquist barrier for linear multistep methods for \(y'=f(t,y)\). Indeed, it is shown how the barrier of Engquist and Osher follows directly from Dahlquist's theorem.