Multi-product splitting and Runge-Kutta-Nyström integrators

Details Multi-product splitting and Runge-Kutta-Nyström integrators Multi-product splitting and Runge-Kutta-Nyström integrators

Apr 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010cemda.106..391c&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 106, Issue 4, pp.391-406

Astronomy and Astrophysics

Astronomy

3

Runge-Kutta-Nyström Integrators, Extrapolated Symplectic Integrators, Arbitrary High-Order Integrators

Scientific paper

The splitting of e h( A+ B) into a single product of e h A and e hB results in symplectic integrators when A and B are classical Lie operators. However, at high orders, a single product splitting, with exponentially growing number of operators, is very difficult to derive. This work shows that, if the splitting is generalized to a sum of products, then a simple choice of the basis product reduces the problem to that of extrapolation, with analytically known coefficients and only quadratically growing number of operators. When a multi-product splitting is applied to classical Hamiltonian systems, the resulting algorithm is no longer symplectic but is of the Runge-Kutta-Nyström (RKN) type. Multi-product splitting, in conjunction with a special force-reduction process, explains why at orders p = 4 and 6, RKN integrators only need p - 1 force evaluations.

Affiliated with

Also associated with

No associations

Rating

Multi-product splitting and Runge-Kutta-Nyström integrators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Multi-product splitting and Runge-Kutta-Nyström integrators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Multi-product splitting and Runge-Kutta-Nyström integrators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1313503