Predictor-Corrector Formula:

A formula which furnishes a first approximation for the iteration procedure described above is called a predictor formula . Formula (7.14) in this connection is called a corrector formula . The above iteration process thus consists in predicting a tentative value of and correcting it (possibly a number of times) by means of the corrector formula. In the interest of minimizing the number of corrections it is clearly desirable to predict as accurately as possible. If the predictor formula is sufficiently accurate, it may make it unnecessary to correct more than once. For these reasons, the Adams-Bashforth formula [(7.3) with diminished by 1] is recommended as an accurate predictor formula in connection with the Adams- Moulton method.

Expressing differences in terms of ordinates, the Adams-Moulton formula (7.9) can be written in the from

(7.15)

where