A formula for numerical solution of differential equations,
![y_(n+1)=y_n+1/6[k_1+(2-sqrt(2))k_2+(2+sqrt(2))k_3+k_4]+O(h^5),](/images/equations/GillsMethod/NumberedEquation1.svg) |
(1)
|
where
 |  |  |
(2)
|
 |  |  |
(3)
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 |  | ![hf[x_n+1/2h,y_n+1/2(-1+sqrt(2))k_1+(1-1/2sqrt(2))k_2]](/images/equations/GillsMethod/Inline9.svg) |
(4)
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 |  | ![hf[x_n+h,y_n-1/2sqrt(2)k_2+(1+1/2sqrt(2))k_3].](/images/equations/GillsMethod/Inline12.svg) |
(5)
|
Gill's Method
See also
Adams' Method, Milne's Method, Predictor-Corrector Methods, Runge-Kutta MethodExplore with Wolfram|Alpha
References
Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 896, 1972.Referenced on Wolfram|Alpha
Gill's MethodCite this as:
Weisstein, Eric W. "Gill's Method." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GillsMethod.html