JSIAM Letters
Online ISSN : 1883-0617
Print ISSN : 1883-0609
ISSN-L : 1883-0617
Articles
Application of the variational principle to deriving energy-preserving schemes for the Hamilton equation
Ai IshikawaTakaharu Yaguchi
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2016 Volume 8 Pages 53-56

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Abstract

In this contribution, we propose a new framework to derive energy-preserving numerical schemes based on the variational principle for Hamiltonian mechanics. We focus on Noether's theorem, which shows that the symmetry with respect to time translation gives the energy conservation law. By reproducing the calculation of the proof of Noether's theorem after discretization using the summation by parts and the discrete gradient, we obtain the scheme and the corresponding discrete energy at the same time. The significant property of efficiency is that the appropriate choice of the discrete gradient makes our schemes explicit if the Hamiltonian is separable.

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© 2016, The Japan Society for Industrial and Applied Mathematics
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