order of accuracy

The power of h that a method's truncation error shrinks like -- read directly off the exponent, or off the slope of a log-log error-vs-h plot.

A method's order of accuracy is the exponent $p$ in a truncation-error bound of the form $Cf^{(k)}(\xi)h^p$ : halving $h$ shrinks an order- $p$ method's error by a factor of $2^p$ . On a log-log plot of error against $h$ , an order- $p$ method's truncation-dominated region traces a straight line of slope $p$ .

Examples

The central-difference formula is order $p=2$ : halving $h$ shrinks its truncation error by a factor of $2^2=4$ , not just 2.