TY - JOUR
T1 - Long Time Energy and Kinetic Energy Conservations of Exponential Integrators for Highly Oscillatory Conservative Systems
AU - Li , Ting
AU - Liu , Changying
AU - Wang , Bin
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 620
EP - 640
PY - 2022
DA - 2022/07
SN - 15
DO - http://doi.org/10.4208/nmtma.OA-2021-0181
UR - https://global-sci.org/intro/article_detail/nmtma/20809.html
KW - Highly oscillatory conservative systems, modulated Fourier expansion, exponential
integrators, long-time conservation.
AB - <p style="text-align: justify;">In this paper, we investigate the long-time near-conservations of energy
and kinetic energy by the widely used exponential integrators to highly oscillatory
conservative systems. The modulated Fourier expansions of two kinds of exponential integrators have been constructed and the long-time numerical conservations
of energy and kinetic energy are obtained by deriving two almost-invariants of the
expansions. Practical examples of the methods are given and the theoretical results
are confirmed and demonstrated by a numerical experiment.</p>