On Energy Conservation by Trigonometric Integrators in the Linear Case with Application to Wave Equations

Authors

  • Ludwig Gauckler Institut für Mathematik, Freie Universität Berlin, Arnimallee 9, D-14195 Berlin, Germany

DOI:

https://doi.org/10.4208/jcm.1903-m2018-0090

Keywords:

Oscillatory Hamiltonian systems, Trigonometric integrators, Energy conservation, Long-time behaviour, Modified energy.

Abstract

Trigonometric integrators for oscillatory linear Hamiltonian differential equations are considered. Under a condition of Hairer & Lubich on the filter functions in the method, a modified energy is derived that is exactly preserved by trigonometric integrators. This implies and extends a known result on all-time near-conservation of energy. The extension can be applied to linear wave equations.

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Published

2020-11-09

Issue

Vol. 38 No. 5 (2020)

Section

Articles