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A sixth order averaged vector field method

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arxiv 1412.5346 v1 pith:HMN4NBEY submitted 2014-12-17 math.NA cs.NA

Haochen Li , Yushun Wang , Mengzhao Qin This is my paper
classification math.NAcs.NA
keywords ordermethodaveragedb-seriesfieldintegratorsixthsubstitution
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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) method to high order. The new integrator turns out to be of order 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.

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