Glossary

Order

The asymptotic rate at which the error decreases.

Definition

Order summarizes the dominant power of the error. If a step method has global error $\mathcal{O}(h^p)$ , halving $h$ reduces the error by about $2^p$ . For root finding, $e_{k+1}\approx C e_k^p$ defines iterative order.

How it is used

Use it to compare refinements, but not as a replacement for cost: RK4 is fourth order, yet uses four evaluations of $f$ per step.