Phase-fitted Discrete Lagrangian Integrators

TL;DR

This paper introduces phase-fitted discrete Lagrangian integrators that enhance accuracy and energy conservation in oscillatory Hamiltonian systems, demonstrated through long-term simulations of the 2-body problem with adaptive error control.

Contribution

It embeds phase fitting into discrete Lagrangian integrators, improving their performance on oscillatory problems and proposing a new adaptive error control technique.

Findings

Enhanced accuracy and energy behavior in Hamiltonian systems

Efficient long-term integration of the 2-body problem up to 100000 periods

Effective adaptive error control based on frequency evaluation

Abstract

Phase fitting has been extensively used during the last years to improve the behaviour 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 behaviour in Hamiltonian systems. Numerical tests on the long term integration (100000 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.