Predictor-Corrector Methods

We have mentioned that the implicit methods tend to yield better results, but they have the obvious disadvantage that they need a good initial estimate for and that one may need to iterate several times if this initial guess is not very accurate.

To overcome this, and to benefit from the positive properties of the implicit method, one often combines an explicit method and an implicit method in a so-called predictor-corrector pair.

The explicit method is then used to predict a value for , and the implicit method is then used once to correct this predicted value.

Often, a Adams-Bashforth and an Adams-Moulton Method of the same order are combined in such a way. Here is an example base on the third order Adams-Bashforth and Adams-Moulton pair.

Example