Before revision:  Even though we focus on wave equations in this paper, the proposed argument is directly applicable to other evolution problems|\mathcal{R}(\Delta t\lambda)|}\leq1\geq1  .
After revision:  Even though we focus on wave equations in this paper, the proposed argument is directly applicable to other evolution problems|\mathcal{R}(\Delta t\lambda)|}\leq1\geq1 is a constant specified by the multistep method itself. Our proof only relies on the stability of the time-integrator and the estimate is independent of the step size \Delta t and the spectrum \sigma(A) .