A Sixth Order Averaged Vector Field Method (Journal of Computational Mathematics, 2018)
In this paper, based on the theory of rooted trees and B-series, we propose the concrete formulas of the substitution law for the trees of order = 5. With the help of the new substitution law, we derive a B-series integrator extending the averaged vector field (AVF) methods for general Hamiltonian system to higher order. The new integrator turns out to be order of six and exactly preserves energy for Hamiltonian systems. Numerical experiments are presented to demonstrate the accuracy and the energy-preserving property of the sixth order AVF method.
Keywords: Hamiltonian systems; B-series; Energy-preserving method; Sixth order AVF method; Substitution law.