Re: This Week's Finds in Mathematical Physics (Week 222)

Robert C. Helling <robert@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
> There are people doing numerical long term stability
> analysis of the solar system. From what I know, they are not just
> taking F=ma and Newton's law of gravity, replace dt by delta t and
> then integrate but use much fancier spectral methods. Could somebody
> please point me to an introduction into these methods?

I don't do this sort of work myself, but the buzzwords you want are
"symplectic ODE integrator". The basic idea is to use an ODE integration
scheme which conserves energy, angular momentum, and maybe other nice
things, up to floating-point roundoff error, rather than just up to
finite differencing error like a standard ODE integrator would do.

For further information, scholar.google.com found about 206 hits for
"symplectic ODE integrator"; several of the ones on the first page
like good intros.

ciao,

--
-- "Jonathan Thornburg -- remove -animal to reply" <jthorn@xxxxxxxxxxxxxxxx>
Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut),
Golm, Germany, "Old Europe" http://www.aei.mpg.de/~jthorn/home.html
"Washing one's hands of the conflict between the powerful and the
powerless means to side with the powerful, not to be neutral."
-- quote by Freire / poster by Oxfam

.