Explicit multistep methods cannot be A-stable
= Explicit multistep methods cannot be A-stable
For an explicit <linear multistep method>, the highest-degree coefficient of $\rho(w)-z\sigma(w)$ is fixed while at least one lower coefficient grows unboundedly with negative real $z$. If all roots stayed in the <unit disk>, the <elementary symmetric polynomials> of those roots would keep every monic coefficient bounded. This contradiction proves that no nontrivial consistent explicit method is <A-stable>.