Talk:Beeman's algorithm

Equations

The second equation doesnot make sense $v(t+\Delta t)=v(t)+v(t)\Delta t+...$ changes in velocity could not be proportional to velocity itself! abakharev 08:04, 15 February 2006 (UTC)[reply]

It looks like the equation was made by someone substituting one of the predictor-corrector modifications and removing the predictor-corrector terms. I removed the reference from the page that links to the incorrect source, and added one with a more complete list. I do not know if the error term is correct, but the source I added seems much more reliable, so I suspect the error term from that source is also correct. Mattopia 08:55, 15 February 2006 (UTC)[reply]

At least it makes sense now. Thanks a lot abakharev 09:01, 15 February 2006 (UTC)[reply]

I was unable to find the original paper from Beeman on it. That second equation looked a little screwy to me to, but I didn't know it well enough to second guess it properly. --Numsgil 12:47, 15 February 2006 (UTC)[reply]

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. --Numsgil 13:02, 15 February 2006 (UTC)[reply]

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 abakharev 16:34, 15 February 2006 (UTC)[reply]

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. --Numsgil 19:11, 15 February 2006 (UTC)[reply]