A HYBRID NUMERICAL-METHOD FOR ANALYSIS OF DYNAMICS OF THE CLASSICAL HAMILTONIAN-SYSTEMS

The numerical integration methods based on the forward and backward ex pansions of solutions in the Taylor series for some classical Hamilton ian systems are considered.-The analytical representations of derivati ves of the Hamiltonian are used for construction of the hybrid schemes of the approximate solutions of the Cauchy problem. The considered ap proach allows us also to study the solutions in the neighborhood of th e singular points of the Hamiltonian. The efficiency of these hybrid i mplicit methods is illustrated on examples of numerical analysis of so lutions for some Hamiltonian systems such as Toda and Henon-Heiles mod els, the system of Coulomb particles, and the three-body gravitational system on a line. A discrete time representation of the evolution of the three-body system on a line connected with constructing pair colli sion transition operators and Poincare sections is discussed.