THE DEVELOPMENT OF VARIABLE-STEP SYMPLECTIC INTEGRATORS, WITH APPLICATION TO THE 2-BODY PROBLEM

The authors develop and test variable step symplectic Runge-Kutta-Nystrom algorithms for the integration of Hamiltonian systems of ordinary differential equations. Numerical experiments suggest that, for symplectic formulae, moving from constant to variable stepsizes results in a marked decrease in efficiency. On the other hand, symplectic formulae with constant stepsizes may outperform available standard (nonsymplectic) variable-step codes. For the model situation consisting in the long-time integration of the two-body problem, our experimental findings are backed by theoretical analysis.