Symmetry Preserving Discretization of the Hamiltonian Systems with Holonomic Constraints

Symmetry preserving difference schemes approximating equations of Hamiltonian systems are presented in this paper. For holonomic systems in the Hamiltonian framework, the symmetrical operators are obtained by solving the determining equations of Lie symmetry with the Maple procedure. The difference...

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Autores principales:	Lili Xia, Mengmeng Wu, Xinsheng Ge
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	lie symmetry preserving difference scheme hamiltonian systems numerical simulation Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/8820ff23bc3d4c8781123e892c01ffeb
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spelling	oai:doaj.org-article:8820ff23bc3d4c8781123e892c01ffeb2021-11-25T18:17:33ZSymmetry Preserving Discretization of the Hamiltonian Systems with Holonomic Constraints10.3390/math92229592227-7390https://doaj.org/article/8820ff23bc3d4c8781123e892c01ffeb2021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2959https://doaj.org/toc/2227-7390Symmetry preserving difference schemes approximating equations of Hamiltonian systems are presented in this paper. For holonomic systems in the Hamiltonian framework, the symmetrical operators are obtained by solving the determining equations of Lie symmetry with the Maple procedure. The difference type of symmetry preserving invariants are constructed based on the three points of the lattice and the characteristic equations. The difference scheme is constructed by using these discrete invariants. An example is presented to illustrate the applications of the results. The solutions of the invariant numerical schemes are compared to the noninvariant ones, the standard and the exact solutions.Lili XiaMengmeng WuXinsheng GeMDPI AGarticlelie symmetry preservingdifference schemehamiltonian systemsnumerical simulationMathematicsQA1-939ENMathematics, Vol 9, Iss 2959, p 2959 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	lie symmetry preserving difference scheme hamiltonian systems numerical simulation Mathematics QA1-939
spellingShingle	lie symmetry preserving difference scheme hamiltonian systems numerical simulation Mathematics QA1-939 Lili Xia Mengmeng Wu Xinsheng Ge Symmetry Preserving Discretization of the Hamiltonian Systems with Holonomic Constraints
description	Symmetry preserving difference schemes approximating equations of Hamiltonian systems are presented in this paper. For holonomic systems in the Hamiltonian framework, the symmetrical operators are obtained by solving the determining equations of Lie symmetry with the Maple procedure. The difference type of symmetry preserving invariants are constructed based on the three points of the lattice and the characteristic equations. The difference scheme is constructed by using these discrete invariants. An example is presented to illustrate the applications of the results. The solutions of the invariant numerical schemes are compared to the noninvariant ones, the standard and the exact solutions.
format	article
author	Lili Xia Mengmeng Wu Xinsheng Ge
author_facet	Lili Xia Mengmeng Wu Xinsheng Ge
author_sort	Lili Xia
title	Symmetry Preserving Discretization of the Hamiltonian Systems with Holonomic Constraints
title_short	Symmetry Preserving Discretization of the Hamiltonian Systems with Holonomic Constraints
title_full	Symmetry Preserving Discretization of the Hamiltonian Systems with Holonomic Constraints
title_fullStr	Symmetry Preserving Discretization of the Hamiltonian Systems with Holonomic Constraints
title_full_unstemmed	Symmetry Preserving Discretization of the Hamiltonian Systems with Holonomic Constraints
title_sort	symmetry preserving discretization of the hamiltonian systems with holonomic constraints
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/8820ff23bc3d4c8781123e892c01ffeb
work_keys_str_mv	AT lilixia symmetrypreservingdiscretizationofthehamiltoniansystemswithholonomicconstraints AT mengmengwu symmetrypreservingdiscretizationofthehamiltoniansystemswithholonomicconstraints AT xinshengge symmetrypreservingdiscretizationofthehamiltoniansystemswithholonomicconstraints
_version_	1718411393169883136

Symmetry Preserving Discretization of the Hamiltonian Systems with Holonomic Constraints

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