The validity of statistical results from N-body calculations.
Abstract
A differential approach is used to investigate the effects of truncation and round-off errors in numerical integration of the N-body equations of motion. For this purpose, the six N equations of motion are integrated by a standard technique without regularization for ensembles of N-body systems with N = 16; all systems initially satisfy the virial theorem, and the members of each ensemble differ among themselves only in the randomly assigned positions and velocities of the N particles. Deviations and errors are defined, the relevant statistical quantities are identified, and various correlations among the statistical quantities are examined. The results indicate that there are three phases in the development of integration errors with calculated N-body systems, that the magnitude of deviations in individual coordinates does not increase linearly with time in all cases, and that the e-folding time increases considerably. It is concluded that significant distortions of the statistical quantities describing N-body systems appear only when the calculated system diverges and that this divergence is readily identifiable through a strong violation of energy conservation.
- Publication:
-
Astronomy and Astrophysics
- Pub Date:
- November 1977
- Bibcode:
- 1977A&A....61..305S
- Keywords:
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- Many Body Problem;
- Star Clusters;
- Statistical Mechanics;
- Stellar Motions;
- Astronomical Models;
- Equations Of Motion;
- Numerical Integration;
- Astronomy