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→Beeman, 1976: equations from the original(?) article, not the same as here. |
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*[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)
== Beeman,
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)
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