Reversible adaptive regularization: perturbed Kepler motion and classical atomic trajectories

Reversible and adaptive integration methods based on Kustaanheimo-Stiefel r egularization and modified Sundman transformations are applied to simulate general perturbed Kepler motion and to compute classical trajectories of at omic systems (e.g. Rydberg atoms). The new family of reversible adaptive re gularization methods also conserves angular momentum and exhibits superior energy conservation and numerical stability in long-time integrations. The schemes are appropriate for scattering, for astronomical calculations of es cape time and long-term stability, and for classical and semiclassical stud ies of atomic dynamics. The components of an algorithm for trajectory calcu lations are described. Numerical experiments illustrate the effectiveness o f the reversible approach.