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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)+4/3h(2y_n^'-y_(n-1)^'+2y_(n-2)^')+O(h^5)
(1)
y_(n+1)=y_(n-1)+1/3h(y_(n-1)^'+4y_n^'+y_(n+1)^')+O(h^5).
(2)

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

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References

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

Referenced on Wolfram|Alpha

Milne's Method

Cite this as:

Weisstein, Eric W. "Milne's Method." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MilnesMethod.html

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