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Volume 40, Issue 1
Long-Time Oscillatory Energy Conservation of Total Energy-Preserving Methods for Highly Oscillatory Hamiltonian Systems

Bin Wang & Xinyuan Wu

DOI: 10.4208/jcm.2008-m2018-0218

J. Comp. Math., 40 (2022), pp. 70-88.

Published online: 2021-11

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  • Abstract

For an integrator when applied to a highly oscillatory system, the near conservation of the oscillatory energy over long times is an important aspect. In this paper, we study the long-time near conservation of oscillatory energy for the adapted average vector field (AAVF) method when applied to highly oscillatory Hamiltonian systems. This AAVF method is an extension of the average vector field method and preserves the total energy of highly oscillatory Hamiltonian systems exactly. This paper is devoted to analysing another important property of AAVF method, i.e., the near conservation of its oscillatory energy in a long term. The long-time oscillatory energy conservation is obtained via constructing a modulated Fourier expansion of the AAVF method and deriving an almost invariant of the expansion. A similar result of the method in the multi-frequency case is also presented in this paper.

  • Keywords

Highly oscillatory Hamiltonian systems, Modulated Fourier expansion, AAVF method, Energy-preserving methods, Long-time oscillatory, Energy conservation.

  • AMS Subject Headings

65P10, 65L05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

wangbinmaths@xjtu.edu.cn (Bin Wang)

xywu@nju.edu.cn (Xinyuan Wu)

  • BibTex
  • RIS
  • TXT
@Article{JCM-40-70, author = {Wang , Bin and Wu , Xinyuan}, title = {Long-Time Oscillatory Energy Conservation of Total Energy-Preserving Methods for Highly Oscillatory Hamiltonian Systems}, journal = {Journal of Computational Mathematics}, year = {2021}, volume = {40}, number = {1}, pages = {70--88}, abstract = {

For an integrator when applied to a highly oscillatory system, the near conservation of the oscillatory energy over long times is an important aspect. In this paper, we study the long-time near conservation of oscillatory energy for the adapted average vector field (AAVF) method when applied to highly oscillatory Hamiltonian systems. This AAVF method is an extension of the average vector field method and preserves the total energy of highly oscillatory Hamiltonian systems exactly. This paper is devoted to analysing another important property of AAVF method, i.e., the near conservation of its oscillatory energy in a long term. The long-time oscillatory energy conservation is obtained via constructing a modulated Fourier expansion of the AAVF method and deriving an almost invariant of the expansion. A similar result of the method in the multi-frequency case is also presented in this paper.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2008-m2018-0218}, url = {http://global-sci.org/intro/article_detail/jcm/19970.html} }
TY - JOUR T1 - Long-Time Oscillatory Energy Conservation of Total Energy-Preserving Methods for Highly Oscillatory Hamiltonian Systems AU - Wang , Bin AU - Wu , Xinyuan JO - Journal of Computational Mathematics VL - 1 SP - 70 EP - 88 PY - 2021 DA - 2021/11 SN - 40 DO - http://doi.org/10.4208/jcm.2008-m2018-0218 UR - https://global-sci.org/intro/article_detail/jcm/19970.html KW - Highly oscillatory Hamiltonian systems, Modulated Fourier expansion, AAVF method, Energy-preserving methods, Long-time oscillatory, Energy conservation. AB -

For an integrator when applied to a highly oscillatory system, the near conservation of the oscillatory energy over long times is an important aspect. In this paper, we study the long-time near conservation of oscillatory energy for the adapted average vector field (AAVF) method when applied to highly oscillatory Hamiltonian systems. This AAVF method is an extension of the average vector field method and preserves the total energy of highly oscillatory Hamiltonian systems exactly. This paper is devoted to analysing another important property of AAVF method, i.e., the near conservation of its oscillatory energy in a long term. The long-time oscillatory energy conservation is obtained via constructing a modulated Fourier expansion of the AAVF method and deriving an almost invariant of the expansion. A similar result of the method in the multi-frequency case is also presented in this paper.

Bin Wang & Xinyuan Wu. (2021). Long-Time Oscillatory Energy Conservation of Total Energy-Preserving Methods for Highly Oscillatory Hamiltonian Systems. Journal of Computational Mathematics. 40 (1). 70-88. doi:10.4208/jcm.2008-m2018-0218
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