Global discretization error ($e_n=y_n-y(t_n)$)

The global error is the difference between the computed and exact solutions after accumulated numerical steps, rather than the local truncation error of a single step started from exact data. An estimate for the stability of a numerical method controls how initial errors and local defects accumulate. For a stable order-$p$ time integrator with starting errors $O(h^p)$, local defects $O(h^{p+1})$ accumulated over $O(1/h)$ steps give global error $O(h^p)$ on a fixed time interval.