Predictor-Corrector Methods
In this lecture we derived Adams-Bashforth and Adams-Moulton
methods via the method of undetermined coefficients.
Adams-Bashforth methods (called Adams method in the book)
are explicit method and are used as predictor for the
Adams-Moulton methods.
If we are not so concerned about the efficient generation of
the formulas (the method of undetermined coefficients is
recommended), then in Maple is is really easy to generate
the Adams-Moulton methods: