Tuesday, September 28, 2021
MLIT Conference Hall, Online seminar via Webex
Ali Baddour (1), M. D. Malykh (1,2)
(1) Peoples’ Friendship University of Russia (RUDN University), (2) Meshcheryakov Laboratory of Information Technologies, Joint Institute for Nuclear Research

On the difference schemes for the many-body problem preserving all algebraic integrals

A new approach to the creation of difference schemes of any order for the many-body problem that preserve all its algebraic integrals is proposed. It is based on the combination of the two ideas: the method of energy quadratization and the rejection of inheritance symplectic structure. Results of the tests with simplest scheme of this class are presented. A flat three-body problem with equal masses is selected for testing. The case when bodies pass close to each other is considered, for which purpose the algorithm of time step scaling near numerical singularities is specially developed. A comparison with the explicit Runge-Kutta method of the 4th order and the simplest simplectic method, the midpoint scheme, was made.

More information on the seminar and the link to connect are available at Indico.