Numerical solution of perturbed Kepler problem using a split operator   technique
  An efficient geometric integrator is proposed for solving the perturbed Kepler motion. This method is stable and accurate over long integration time, which makes it appropriate for treating problems in astrophysics, like solar system simulations, and atomic and molecular physics, like classical simulations of highly excited atoms in external fields. The key idea is to decompose the hamiltonian in solvable parts and propagate the system according to each term. Two case studies, the Kepler atom in an uniform field and in a monochromatic field, are presented and the errors are analyzed. 
G. S. Balaraman and D. Vrinceanu