High order symplectic integrators for perturbed Hamiltonian systems

Details High order symplectic integrators for perturbed Hamiltonian systems High order symplectic integrators for perturbed Hamiltonian systems

2000-05-04

arxiv.org/abs/astro-ph/0005074v1

Astronomy and Astrophysics

Astrophysics

24 pages, 6 figurres

Scientific paper

We present a class of symplectic integrators adapted for the integration of perturbed Hamiltonian systems of the form $H=A+\epsilon B$. We give a constructive proof that for all integer $p$, there exists an integrator with positive steps with a remainder of order $O(\tau^p\epsilon +\tau^2\epsilon^2)$, where $\tau$ is the stepsize of the integrator. The analytical expressions of the leading terms of the remainders are given at all orders. In many cases, a corrector step can be performed such that the remainder becomes $O(\tau^p\epsilon +\tau^4\epsilon^2)$. The performances of these integrators are compared for the simple pendulum and the planetary 3-Body problem of Sun-Jupiter-Saturn.

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