Embedded operator splitting methods for perturbed systems

Hanno Rein

doi:10.1093/mnras/staa240

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Embedded operator splitting methods for perturbed systems

2020-01-28

Hanno Rein *

DOI：10.1093/mnras/staa240

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Abstract

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It is common in classical mechanics to encounter systems whose Hamiltonian H is the sum of an often exactly integrable Hamiltonian Hu and a small perturbation EH1 with e K< 1, Such near-integrability can be exploited to construct particular] y accurate operator splitting methods to solve the equations of motion of H. However, in many cases, for example in problems related to planetary motion, it is computationally expensive to obtain the exact solution to Ho, In this paper, we present a new family of embedded operator splitting (EOS) methods which do not use the exact solution to Ho, but rather approximate it with yet another, EOS method, Our new methods have all the desirable properties of classical methods which solve Ho, directly. But in addition they are very easy to implement and in some cases faster, When applied to the problem of planetary motion, our EOS methods have error scalings identical to that of the often used Wisdom-Holman method hut do not require a Kepler solver, nor any coordinate transformations, or the allocation of memory. The only two problem specific functions that need to be implemented are the straightforward kick and drift steps typically used in the standard second -order leap -frog method.

Keywords:

gravitation

methods: numerical

planets and satellites: dynamical evolution and stability

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