TY - JOUR
T1 - On Energy Conservation by Trigonometric Integrators in the Linear Case with Application to Wave Equations
AU - Gauckler , Ludwig
JO - Journal of Computational Mathematics
VL - 5
SP - 705
EP - 714
PY - 2020
DA - 2020/04
SN - 38
DO - http://doi.org/10.4208/jcm.1903-m2018-0090
UR - https://global-sci.org/intro/article_detail/jcm/16665.html
KW - Oscillatory Hamiltonian systems, Trigonometric integrators, Energy conservation, Long-time behaviour, Modified energy.
AB - <p style="text-align: justify;">Trigonometric integrators for oscillatory linear Hamiltonian differential equations are
considered. Under a condition of Hairer &amp; 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.</p>