Difference discrete variational principles, Euler-Lagrange cohomology and symplectic, multisymplectic structures III: Application to symplectic and multisymplectic algorithms

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	Difference discrete variational principles, Euler-Lagrange cohomology and symplectic, multisymplectic structures III: Application to symplectic and multisymplectic algorithms
	Guo, HY ; Li, YQ ; Wu, K ; Wang, SK
	2002-03-15
发表期刊	COMMUNICATIONS IN THEORETICAL PHYSICS
ISSN	0253-6102
卷号	37 期号:3 页码:257-264
摘要	In the previous papers I and II, we have studied the difference discrete variational principle and the Euler-Lagrange cohomology in the framework of multi-parameter differential approach. We have gotten the difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of classical mechanics and held theory as well as the difference discrete versions for the Euler Lagrange cohomology and applied them to get the necessary and sufficient condition for the symplectic or multisymplectic geometry preserving properties in both the Lagrangian and Hamiltonian formalisms. In this paper, we apply the difference discrete variational principle and Euler-Lagrange cohomological approach directly to the symplectic and multisymplectic algorithms, We will show that either Hamiltonian schemes or Lagrangian ones in both the symplectic and multisymplectic algorithms are variational integrators and their difference discrete symplectic structure-preserving properties can always be established not only in the solution space but also in the function space if and only if the related closed Euler-Lagrange cohomological conditions are satisfied.
关键词	discrete variation Euler-Lagrange cohomology symplectic algorithm multisymplectic algorithm
语种	英语
WOS研究方向	Physics
WOS类目	Physics, Multidisciplinary
WOS记录号	WOS:000174671700001
出版者	INT ACADEMIC PUBL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/17520
专题	中国科学院数学与系统科学研究院
通讯作者	Guo, HY
作者单位	1.Acad Sinica, Inst Theoret Phys, Beijing 100080, Peoples R China 2.Capital Normal Univ, Dept Math, Beijing 100037, Peoples R China 3.Acad Sinica, Acad Math & Syst Sci, Inst Appl Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Guo, HY,Li, YQ,Wu, K,et al. Difference discrete variational principles, Euler-Lagrange cohomology and symplectic, multisymplectic structures III: Application to symplectic and multisymplectic algorithms[J]. COMMUNICATIONS IN THEORETICAL PHYSICS,2002,37(3):257-264.
APA	Guo, HY,Li, YQ,Wu, K,&Wang, SK.(2002).Difference discrete variational principles, Euler-Lagrange cohomology and symplectic, multisymplectic structures III: Application to symplectic and multisymplectic algorithms.COMMUNICATIONS IN THEORETICAL PHYSICS,37(3),257-264.
MLA	Guo, HY,et al."Difference discrete variational principles, Euler-Lagrange cohomology and symplectic, multisymplectic structures III: Application to symplectic and multisymplectic algorithms".COMMUNICATIONS IN THEORETICAL PHYSICS 37.3(2002):257-264.