Five-point formulae

The three-point formulae have errors proportional to [Maple Math] . One can also construct five-point formulae with an error term proportional to [Maple Math] . A derivation is given below as an illustration, and is basically the same as the three point formulae.

Derivation

The centered five-point difference formula is given by:

[Maple Math]

Let us look at an example of its use:

Example