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Volume 41, Issue 3
Two Novel Classes of Arbitrary High-Order Structure-Preserving Algorithms for Canonical Hamiltonian Systems

Yonghui Bo, Wenjun Cai & Yushun Wang

DOI: 10.4208/jcm.2108-m2021-0076

J. Comp. Math., 41 (2023), pp. 395-414.

Published online: 2023-02

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  • Abstract

In this paper, we systematically construct two classes of structure-preserving schemes with arbitrary order of accuracy for canonical Hamiltonian systems. The one class is the symplectic scheme, which contains two new families of parameterized symplectic schemes that are derived by basing on the generating function method and the symmetric composition method, respectively. Each member in these schemes is symplectic for any fixed parameter. A more general form of generating functions is introduced, which generalizes the three classical generating functions that are widely used to construct symplectic algorithms. The other class is a novel family of energy and quadratic invariants preserving schemes, which is devised by adjusting the parameter in parameterized symplectic schemes to guarantee energy conservation at each time step. The existence of the solutions of these schemes is verified. Numerical experiments demonstrate the theoretical analysis and conservation of the proposed schemes.

  • Keywords

Hamiltonian systems, Symplectic schemes, Energy-preserving schemes, EQUIP schemes, Generating function methods, Symmetric composition methods.

  • AMS Subject Headings

65L05, 65P10, 70H15, 70H20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

boyonghui@ahnu.edu.cn (Yonghui Bo)

caiwenjun@njnu.edu.cn (Wenjun Cai)

wangyushun@njnu.edu.cn (Yushun Wang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-41-395, author = {Bo , YonghuiCai , Wenjun and Wang , Yushun}, title = {Two Novel Classes of Arbitrary High-Order Structure-Preserving Algorithms for Canonical Hamiltonian Systems}, journal = {Journal of Computational Mathematics}, year = {2023}, volume = {41}, number = {3}, pages = {395--414}, abstract = {

In this paper, we systematically construct two classes of structure-preserving schemes with arbitrary order of accuracy for canonical Hamiltonian systems. The one class is the symplectic scheme, which contains two new families of parameterized symplectic schemes that are derived by basing on the generating function method and the symmetric composition method, respectively. Each member in these schemes is symplectic for any fixed parameter. A more general form of generating functions is introduced, which generalizes the three classical generating functions that are widely used to construct symplectic algorithms. The other class is a novel family of energy and quadratic invariants preserving schemes, which is devised by adjusting the parameter in parameterized symplectic schemes to guarantee energy conservation at each time step. The existence of the solutions of these schemes is verified. Numerical experiments demonstrate the theoretical analysis and conservation of the proposed schemes.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2108-m2021-0076}, url = {http://global-sci.org/intro/article_detail/jcm/21390.html} }
TY - JOUR T1 - Two Novel Classes of Arbitrary High-Order Structure-Preserving Algorithms for Canonical Hamiltonian Systems AU - Bo , Yonghui AU - Cai , Wenjun AU - Wang , Yushun JO - Journal of Computational Mathematics VL - 3 SP - 395 EP - 414 PY - 2023 DA - 2023/02 SN - 41 DO - http://doi.org/10.4208/jcm.2108-m2021-0076 UR - https://global-sci.org/intro/article_detail/jcm/21390.html KW - Hamiltonian systems, Symplectic schemes, Energy-preserving schemes, EQUIP schemes, Generating function methods, Symmetric composition methods. AB -

In this paper, we systematically construct two classes of structure-preserving schemes with arbitrary order of accuracy for canonical Hamiltonian systems. The one class is the symplectic scheme, which contains two new families of parameterized symplectic schemes that are derived by basing on the generating function method and the symmetric composition method, respectively. Each member in these schemes is symplectic for any fixed parameter. A more general form of generating functions is introduced, which generalizes the three classical generating functions that are widely used to construct symplectic algorithms. The other class is a novel family of energy and quadratic invariants preserving schemes, which is devised by adjusting the parameter in parameterized symplectic schemes to guarantee energy conservation at each time step. The existence of the solutions of these schemes is verified. Numerical experiments demonstrate the theoretical analysis and conservation of the proposed schemes.

Yonghui Bo, Wenjun Cai & Yushun Wang. (2023). Two Novel Classes of Arbitrary High-Order Structure-Preserving Algorithms for Canonical Hamiltonian Systems. Journal of Computational Mathematics. 41 (3). 395-414. doi:10.4208/jcm.2108-m2021-0076
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