Local truncation error
= Local truncation error
The local truncation error is the defect left when exact solution values are inserted into a numerical update. For a one-step method started from the exact solution,
$$
\tau_{n+1}
=y(t_{n+1})-y(t_n)-h\phi(t_n,y(t_n),h).
$$
A local error $O(h^{p+1})$ generally leads to global error $O(h^p)$ under a uniform stability bound.