Phase-fitted discrete Lagrangian integrators

Phase fitting has been extensively used during the last years to improve the behavior of numerical integrators on oscillatory problems. In this work, the benefits of the phase fitting technique are embedded in discrete Lagrangian integrators. The results show improved accuracy and total energy behavior in Hamiltonian systems. Numerical tests on the long term integration (105 periods) of the 2-body problem with eccentricity even up to 0.95 show the efficiency of the proposed approach. Finally, based on a geometrical evaluation of the frequency of the problem, a new technique for adaptive error control is presented.