iv) The Generalized Milne-Simpson Method:

Here we have

(7.18)

where

(7.19)

Formula (7.18) resembles the Adams-Moulton formula in being implicit. However, the integration is now over two steps, which may cause weak stability. On the other hand, the method is, for comparable , more accurate than any of the methods previously considered. This is true in particular in the case , which is known as the Milne method. The reason why it is more accurate will be understood by studying the coefficients . Their generating function is given by