TOPICS
Search

Gill's Method


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),
(1)

where

k_1=hf(x_n,y_n)
(2)
k_2=hf(x_n+1/2h,y_n+1/2k_1)
(3)
k_3=hf[x_n+1/2h,y_n+1/2(-1+sqrt(2))k_1+(1-1/2sqrt(2))k_2]
(4)
k_4=hf[x_n+h,y_n-1/2sqrt(2)k_2+(1+1/2sqrt(2))k_3].
(5)

See also

Adams' Method, Milne's Method, Predictor-Corrector Methods, Runge-Kutta Method

Explore 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 Method

Cite this as:

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

Subject classifications