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==Equations==
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== Error term ==
The first source says the error term on velocity is O(dt^4), whereas the other two sources claim O(dt^3). The best step is to probably find Beeman's original paper on the algorithm and be certain one way or another. --[[User:Numsgil|Numsgil]] 13:02, 15 February 2006 (UTC)
*The errors of derivative are almost universally one order worse than the errors of the main value. So I will be surprised if the order would be dt^4 for both position and velocity. I took the liberty to edit the formula, it would be still worth to find the original paper anyway [[User:Alex Bakharev|abakharev]] 16:34, 15 February 2006 (UTC)
::I think it's O(dt^3) also, however velocity verlet is an example of an algorithm with the same order of error for position and velocity. --[[User:Numsgil|Numsgil]] 19:11, 15 February 2006 (UTC)
== Bad link ==
*[http://mse-jl1.eng.ohio-state.edu/Archive/Papers/05/Li05-2.8.pdf Basic Molecular Dynamics] - page and pdf file were deleted. --[[User:Vadikus|Vadikus]] ([[User talk:Vadikus|talk]]) 10:51, 21 October 2008 (UTC)
::It's now at [http://mt.seas.upenn.edu/Archive/Papers/05/Li05-2.8.pdf UPenn].--[[User:LutzL|LutzL]] ([[User talk:LutzL|talk]]) 10:45, 23 June 2011 (UTC)
== Beeman, 1976 ==
I've put a citation for the original Beeman paper into the source (hidden in a comment). If someone who has access to J. Comp. Phys. could please have a look at it and confirm that it is an appropriate reference, then that should save a little bit of time putting the details together! --[[User:Philtweir|Philtweir]] ([[User talk:Philtweir|talk]]) 12:34, 16 June 2010 (UTC)
:The equations of the order 3 method in the paper are
::<math>\begin{align}
\text{predictor }&\\
r_{n+1}&=r_n+hv_n+\frac{h^2}{6}(4a_n-a_{n-1})+\frac{h^4}{8}r_n^{(4)};\\
\text{corrector }& \text{ (after computation of }a_{n+1})\\
r_{n+1}&=r_n+hv_n+\frac{h^2}{6}(a_{n+1}-2a_n)-\frac{h^4}{12}r_n^{(4)};\\
hv_{n+1}&=r_{n+1}-r_n+\frac{h^2}{6}(2a_{n+1}+a_n)-\frac{h^4}{24}r_n^{(4)}.
\end{align}</math>
:Additionally, methods of order 4 and 5 are given and numerically compared to Verlet, Adams-Multon-Bashford multistep, Rahman and Nordsiek methods. Verlet is not used in the leapfrog or velocity Verlet variants, in this situation Beeman's third order method appeared more stable for larger steplengths. The ''x'' steps are the same as in the article, the corrector steps are at odds.--[[User:LutzL|LutzL]] ([[User talk:LutzL|talk]]) 14:52, 6 September 2010 (UTC)
==Assessment comment==
{{Substituted comment|length=253|lastedit=20070510072947|comment=Seems to have the basic info (except for stability), but needs a lot of editing. What equation is solved? What is the point of the predictor/corrector section? [[User:Jitse Niesen|Jitse Niesen]] ([[User talk:Jitse Niesen|talk]]) 07:29, 10 May 2007 (UTC)}}
Substituted at 01:48, 5 May 2016 (UTC)
== Who is Beeman? ==
The introduction mentions "Beeman" several times but never includes his or her first name. [[User:The-erinaceous-one|The-erinaceous-one]] ([[User talk:The-erinaceous-one|talk]]) 07:14, 1 August 2020 (UTC)
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