Stepize control algorithms for composition ODE solvers

The purpose of this research is to study the symplecticity and reversibility of Hamiltonian systems simulated with adaptive step control algorithms. We consider several composition ODE solvers of different accuracy order using H. Yoshida composition formulas and semi-implicit basic methods. The comparison of three adaptive step control algorithms with different local truncation error estimation techniques is given. A full system energy behavior and dynamics of a solution phase space are studied in a series of computer experiments.