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Volume 15, Issue 3
Long Time Energy and Kinetic Energy Conservations of Exponential Integrators for Highly Oscillatory Conservative Systems

Ting Li, Changying Liu & Bin Wang

DOI: 10.4208/nmtma.OA-2021-0181

Numer. Math. Theor. Meth. Appl., 15 (2022), pp. 620-640.

Published online: 2022-07

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  • Abstract

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.

  • Keywords

Highly oscillatory conservative systems, modulated Fourier expansion, exponential integrators, long-time conservation.

  • AMS Subject Headings

65P10, 65L05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-15-620, author = {Li , TingLiu , Changying and Wang , Bin}, title = {Long Time Energy and Kinetic Energy Conservations of Exponential Integrators for Highly Oscillatory Conservative Systems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2022}, volume = {15}, number = {3}, pages = {620--640}, abstract = {

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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2021-0181}, url = {http://global-sci.org/intro/article_detail/nmtma/20809.html} }
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 -

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.

Li , TingLiu , Changying and Wang , Bin. (2022). Long Time Energy and Kinetic Energy Conservations of Exponential Integrators for Highly Oscillatory Conservative Systems. Numerical Mathematics: Theory, Methods and Applications. 15 (3). 620-640. doi:10.4208/nmtma.OA-2021-0181
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