= Global discretization error
{title2=$e_n=y_n-y(t_n)$}
= Global error
{synonym}
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.
Back to article page
