Milne Predictor Corrector Formula

There are a number of important predictor-corrector equations, including equations (3.3.15) and (3.3.18), which are the fourth-order Milne predictor-corrector formulas. 

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... 

Values of y , y , y 2 and y 3 are required to caleulate y , . Milne s method uses Newton-Cotes formula for the predictor and Simpson s rule for the corrector. 

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