The local truncation error is thus in and in .

If the equations are of a restricted type, then these methods can be more practical. The system

with first derivatives absent frequently occurs in celestial mechanics. In this case and .

Consequently, (4.8) is replaced by

(4.10)

while is given by

(4.11)

The first four terms of both (4.10) and (4.11) can be made to agree with the Taylor's series terms by choosing