Order conditions for a linear multistep method
= Order conditions for a linear multistep method
A linear multistep method has order $p$ exactly when
$$
\sum_j\alpha_jj^q=q\sum_j\beta_jj^{q-1}
$$
for $0\leq q\leq p$, with the right side interpreted as zero for $q=0$, and the identity first fails at $q=p+1$.