Details

The predictor-corrector method is a two-step technique. First, the prediction step calculates a rough approximation of the desired quantity, typically using an explicit method. Second, the corrector step refines the initial approximation in another way, typically with an implicit method.

The two-step Adams predictor-corrector method:

(predictor step: two-step Adams–Bashforth)

(corrector step: two-step Adams–Moulton)

The four-step Adams predictor-corrector method uses the four-step Adams–Bashforth and Adams-Moulton methods together:

(predictor step) (corrector step)

The two-step and four-step Adams methods require two and four initial values to start the calculation, respectively. These later can be obtained by using other methods, for example Euler or Runge–Kutta.