from which we derive the recurrence relations

The numerical values of are given as under:

Special case q=1 of Nystrom's method:

In this case, we have

or

which gives the mid-point method. Since , it yields the same accuracy as could be expected from taking , which accounts for some of the popularity of the method. The mid-point rule has also been used as a predictor formula for the trapezoidal rule (Adams-Moulton method with q=1). For general the Nystrom method may be used as a predictor formula for the generalized Milne- Simpson method to be discussed now.