Re: NDSolve Percision

*To*: mathgroup at smc.vnet.net*Subject*: [mg85493] Re: NDSolve Percision*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Wed, 13 Feb 2008 04:02:15 -0500 (EST)*Organization*: Uni Leipzig*References*: <fopbtt$c4m$1@smc.vnet.net>*Reply-to*: kuska at informatik.uni-leipzig.de

Hi, have you used Method -> {"SymplecticPartitionedRungeKutta"} ?? to avoid that ? An non-symplectic method *must* loss the energy of the system, this has nothing to do with the Precision, this has to do with the fact that a normal numerical method for initial value problems is designed to reduce the local error and not to preserve a global quantity like the energy. Regards Jens Alex Cloninger wrote: > So I'm running a program that is trying to use NDSolve and parametrically plot the results. The result is periodic, so it should cycle back on itself with a period of 2Pi. It does that, but if I run from {t,0,20Pi} is starts to miss the initial point by more and more. Basically, it's spiraling outward at a slow but unwanted rate. This will be a problem for when I increase the difficulty of the function. > > How do I increase the precision of NDSolve to make it keep more decimals and make the answer more accurate? > > The function is > > solution = NDSolve[{x'[t] == 2p[t], x[0] == 2, > p'[t] == -2x[t],p[0] == N[Sqrt[-3], 50]}, {x, p}, {t,0,20Pi}] > > If you could help me out, I'd really appreciate it. Thanks. >