From: spellucci@mathematik.tu-darmstadt.de (Peter Spellucci)
Subject: Re: Runga Kutta Gill
Date: 4 Dec 2001 15:22:37 GMT
Newsgroups: sci.math.num-analysis
Summary: Runga Kutta Gill method of solving ODE numerically

In article <3c0b0f4f$1_2@news.ghg.net>,
 "Don" <dpearson@ghg.net> writes:
|> I've been using a formulation documented in "Fundamentals of Astrodynamics"
|> for Runga Kutta Gill and now believe there may be an error in the printed
|> equation for the 4th step, which reads:
|> 
|> k4 = h * f (t + h,  x - k2/sqrt(2) + k3(1+(sqrt(0.5)))
|> 
|> Does anyone have another (preferrably online) reference to the Runga Kutta
|> Gill formulation?

not online, but
1) Henrici: discrete variable methods in ordinary differential equations;
wiley; corr. print 1968 , page 122
2) hairer&norsett&wanner; solving ordinary differential equations I, 
springer, 1st printing 1986, page 138
(in the condensed form of the original paper of gill). 

henrici   (I translate to your notation. he does not incorporate the "h*"
           into the definition of the k_i)
 k4 = h*f(t+h,x+(p4-p5-p6)*k1 + p5*k2 + p6*k3)
 p4=1 p5=1-t p6=t and t=1-1/sqrt(2) hence the printing error above is in p5 
 and p6.

to cite from hairer et alii:
today, in large high-sped computers this method is no longer used but 
could still be of interest for very high dimensional equations. 

the essential contribution: the method needs only two additional vectors for 
computing the next x.

hope that helps
peter
============================================================================== 

From: "Dann Corbit" <dcorbit@connx.com>
Subject: Re: Runga Kutta Gill
Date: Mon, 3 Dec 2001 13:55:02 -0800
Newsgroups: sci.math.num-analysis

"Don" <dpearson@ghg.net> wrote in message news:3c0b0f4f$1_2@news.ghg.net...
[quote of original message deleted --djr]

http://mathworld.wolfram.com/GillsMethod.html

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