Adams Closed Formulas

Adams Closed Formulas require an iterative method to solve for y, since the right side of the expression requires a value for f,. The iteration of estimating y, evaluating f, and obtaining a new estimate of y is repeated until it converges to the desired accuracy. The general formula is... 

A combination of open- and closed-type formulas is referred to as the predictor-corrector method. First the open equation (the predictor) is used to estimate a value for y,, this value is then inserted into the right side of the corrector equation (the closed formula) and iterated to improve the accuracy of y. The predictor-corrector sets may be the low-order modified (open) and improved (closed) Euler equations, the Adams open and closed formulas, or the Milne method, which gives the following system... 

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