Milne's Method

A Predictor-Corrector Method for solution of Ordinary Differential Equations. The third-order equations for predictor and corrector are

$$y_{n+1} = y_{n-3}+{\textstyle{4\over 3}}h(2y_n'-y_{n-1}'+2y_{n-2}')+{\mathcal O}(h^5)$$

$$y_{n+1} = y_{n-1}+{\textstyle{1\over 3}}h(y_{n-1}'+4y_n'+y_{n+1}')+{\mathcal O}(h^5).$$

Abramowitz and Stegun (1972) also give the fifth order equations and formulas involving higher derivatives.

See also Adams' Method, Gill's Method, Predictor-Corrector Methods, Runge-Kutta Method

References

Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 896-897, 1972.