Order of a numerical method
= Order of a numerical method
{title2=$R_h=O(h^{p+1})$}
For a time-stepping formula written with an unscaled step residual $R_h$, order at least $p$ means that substituting a smooth exact solution gives $R_h=O(h^{p+1})$. Under the relevant <stability of a numerical method> assumptions and starting errors $O(h^p)$, this produces <global error> $O(h^p)$. Residuals divided by the step size instead use the equivalent convention $O(h^p)$.