Am Montag, 9. Mai 2005 05:38 schrieb Greg Buchholz:
Daniel Fischer wrote:
One question: the energy of the system should be constant - that little physics I know. What I don't know is whether the change in energy in this simulation is within usual, reasonable bounds or not. If not, is it due to a too long time interval or should one use a more sophisticated algorithm?
The change in energy is from round-off error caused by floating point arithmetic. For this particular test, the shootout requires everyone to use the same algorithm. So the error is expected.
Greg Buchholz
Well, I think most of the change is due to the algorithm, which gives a rather crude approximation to the actual solution of the ODE. This is backed by trying different values of dt (actually tested with Java, because that uses hardly any memory at all and is much much faster). For the tests, dt * k = 20, dt is the argument: dafis@linux:~/Documents/haskell/dmitri/Greg/Bodies> java PlanSys 0.1 -0.1690751638285245 -0.16877178579767274 dafis@linux:~/Documents/haskell/dmitri/Greg/Bodies> java PlanSys 0.05 -0.1690751638285245 -0.16899653420881677 dafis@linux:~/Documents/haskell/dmitri/Greg/Bodies> java PlanSys 0.025 -0.1690751638285245 -0.1690547211965566 ... dafis@linux:~/Documents/haskell/dmitri/Greg/Bodies> java PlanSys 0.00001 -0.1690751638285245 -0.16907516338916015 dafis@linux:~/Documents/haskell/dmitri/Greg/Bodies> java PlanSys 0.000005 -0.1690751638285245 -0.16907516360969982 dafis@linux:~/Documents/haskell/dmitri/Greg/Bodies> time java PlanSys 0.0000025 -0.1690751638285245 -0.16907516371932937 real 1m42.464s user 1m39.900s sys 0m2.540s To me it looks like finer granularity on the time scale is not yet consumed by rounding errors (and since we never divide by small numbers, I wouldn't expect any dramatic effects for a while). If the algorithm - including dt - is prescribed, fine, but I wonder what sort of deviation physicists would consider acceptable. For dt = 0.01, k = 2000 we have a relative error of about 2*10^(-5), is that within accepted bounds or not? (Any physicists hang about here?) Cheers, Daniel