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A Sixth Order Averaged Vector Field Method

A Sixth Order Averaged Vector Field Method
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Year:    2016

Author:    Haochen Li, Yushun Wang, Mengzhao Qin

Journal of Computational Mathematics, Vol. 34 (2016), Iss. 5 : pp. 479–498

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1601-m2015-0265

Journal of Computational Mathematics, Vol. 34 (2016), Iss. 5 : pp. 479–498

Published online:    2016-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Hamiltonian systems B-series Energy-preserving method Sixth order AVF method Substitution law.

Author Details

Haochen Li

Yushun Wang

Mengzhao Qin

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