3. Some further Special methods:

Further useful formulas can be derived by doubling the step K, analogously to the doubling of the step in the derivation of the Nystrom and Milne-Simpson methods for first order equations. By taking , we obtain the formula

(7.48)

where the coefficients are given by

(7.49)

Again, the method of generating function is used to obtain the coefficients as follows:

On integration, one finds that

(7.50)

or

This gives