 Solution

A one-step or linear multistep method has order $p$ if, when the exact sufficiently smooth solution is substituted for the numerical values, its unscaled local truncation error is $O(h^{p+1})$, and this estimate is not generally $O(h^{p+2})$. For a stable method this corresponds to a global error of order $O(h^p)$ on a fixed time interval.