Numerical Integration of the Polygonal n-body Problem in High Precision Arithmetic

Details Numerical Integration of the Polygonal n-body Problem in High Precision Arithmetic Numerical Integration of the Polygonal n-body Problem in High Precision Arithmetic

May 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007padeu..19..247p&link_type=abstract

Publications of the Astronomy Department of the Eötvös University (PADEU), 2007, ISBN 963 463 557, Vol. 19. Edited by B. Érdi a

Astronomy and Astrophysics

Astronomy

Scientific paper

The paper presents a computer algebra program dedicated to the synthesis and generation of numerical code for the integration of the n-body problem using an arbitrary precision arithmetic library. The program is able to apply several numerical methods specified in the high level programming language of the computer algebra system and to generate efficient low level code. The library is tested in the numerical integration of the general n-body problem starting with the initial conditions where the equal mass bodies having equal velocities are placed at the vertices and in the center of a regular polygon. In this case the problem has analytical solution but proves to be hard to integrate numerically in standard double precision due to the instability of the symmetric configuration.

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