N-body problem solution with composition numerical integration methods

The subject of this paper is the experimental study of the composition numerical integration methods while solving the N-body problem. Various composition methods based on symmetric second order Verlet method are considered. Step size control algorithm for these methods is described. The principles for experimental estimation of the time reversibility for composition methods with fixed and adaptive integration steps is described. The results six-body problem simulation by composition method of accuracy order 6 and Runge-Kutta 45 method are compared. Conclusions about the effectiveness of proposed algorithms for long-term simulation of the chosen problem are given. Study shows that semi-implicit composition methods have greater numerical stability for N-body problem simulation than the explicit Runge-Kutta methods. It is shown that the semi-implicit composition methods with fixed integration step are time-reversible, but they lose this property in a case of adaptive step size.