Symmetric multistep methods over long times
Ernst Hairer and Christian Lubich
Abstract.
For computations of planetary motions with special
linear multistep methods
an excellent long-time behaviour is reported in the literature,
without a theoretical explanation.
Neither the
total energy nor the angular momentum exhibit secular error terms.
In this paper we completely explain this behaviour by studying
the modified equation of these methods and by
analyzing the remarkably stable propagation of parasitic solution components.
Key Words.
Linear multistep method,
Hamiltonian system,
N-body system,
energy conservation, conservation of angular momentum,
symplecticity, invariant tori, linear error growth,
backward error analysis, modified differential equation,
modulated Fourier expansion.