So the object is to match

with the Taylor expansion

Equating coefficients of like powers of **h** in the above
expressions for **R** and **T**, we are able to obtain agreement in terms involving
and :

If we choose , an arbitrary parameter, these equations can be solved exactly to give

Combining all of this gives a one-step method of order **p = 2** if
and **f** is sufficiently smooth. We state this in the following algorithm.