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Volume 17, Issue 1
Energy-Preserving Parareal-RKN Algorithms for Hamiltonian Systems

Zhen Miao, Bin Wang & Yaolin Jiang

DOI: 10.4208/nmtma.OA-2023-0081

Numer. Math. Theor. Meth. Appl., 17 (2024), pp. 121-144.

Published online: 2024-02

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  • Abstract

In this paper, we formulate and analyse a kind of parareal-RKN algorithms with energy conservation for Hamiltonian systems. The proposed algorithms are constructed by using the ideas of parareal methods, Runge-Kutta-Nyström (RKN) methods and projection methods. It is shown that the algorithms can exactly preserve the energy of Hamiltonian systems. Moreover, the convergence of the integrators is rigorously analysed. Three numerical experiments are carried out to support the theoretical results presented in this paper and show the numerical behaviour of the derived algorithms.

  • Keywords

Parareal methods, Runge-Kutta-Nyström methods, Hamiltonian systems, energy conservation.

  • AMS Subject Headings

65L05, 65L20, 65P10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-17-121, author = {Miao , ZhenWang , Bin and Jiang , Yaolin}, title = {Energy-Preserving Parareal-RKN Algorithms for Hamiltonian Systems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2024}, volume = {17}, number = {1}, pages = {121--144}, abstract = {

In this paper, we formulate and analyse a kind of parareal-RKN algorithms with energy conservation for Hamiltonian systems. The proposed algorithms are constructed by using the ideas of parareal methods, Runge-Kutta-Nyström (RKN) methods and projection methods. It is shown that the algorithms can exactly preserve the energy of Hamiltonian systems. Moreover, the convergence of the integrators is rigorously analysed. Three numerical experiments are carried out to support the theoretical results presented in this paper and show the numerical behaviour of the derived algorithms.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2023-0081}, url = {http://global-sci.org/intro/article_detail/nmtma/22913.html} }
TY - JOUR T1 - Energy-Preserving Parareal-RKN Algorithms for Hamiltonian Systems AU - Miao , Zhen AU - Wang , Bin AU - Jiang , Yaolin JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 121 EP - 144 PY - 2024 DA - 2024/02 SN - 17 DO - http://doi.org/10.4208/nmtma.OA-2023-0081 UR - https://global-sci.org/intro/article_detail/nmtma/22913.html KW - Parareal methods, Runge-Kutta-Nyström methods, Hamiltonian systems, energy conservation. AB -

In this paper, we formulate and analyse a kind of parareal-RKN algorithms with energy conservation for Hamiltonian systems. The proposed algorithms are constructed by using the ideas of parareal methods, Runge-Kutta-Nyström (RKN) methods and projection methods. It is shown that the algorithms can exactly preserve the energy of Hamiltonian systems. Moreover, the convergence of the integrators is rigorously analysed. Three numerical experiments are carried out to support the theoretical results presented in this paper and show the numerical behaviour of the derived algorithms.

Zhen Miao, Bin Wang & Yaolin Jiang. (2024). Energy-Preserving Parareal-RKN Algorithms for Hamiltonian Systems. Numerical Mathematics: Theory, Methods and Applications. 17 (1). 121-144. doi:10.4208/nmtma.OA-2023-0081
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