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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; Guo, HY , Acad Sinica, Inst Theoret Phys, POB 2735, Beijing 100080, Peoples R China.
2002
发表期刊COMMUNICATIONS IN THEORETICAL PHYSICS
ISSN0253-6102
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.
部门归属Acad Sinica, Inst Theoret Phys, Beijing 100080, Peoples R China; Capital Normal Univ, Dept Math, Beijing 100037, Peoples R China; Acad Sinica, Acad Math & Syst Sci, Inst Appl Math, Beijing 100080, Peoples R China
学科领域Physics
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收录类别SCI
WOS记录号WOS:000174671700001
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被引频次:21[WOS]   [WOS记录]     [WOS相关记录]
文献类型期刊论文
条目标识符http://ir.itp.ac.cn/handle/311006/13565
专题理论物理所1978-2010年知识产出
通讯作者Guo, HY , Acad Sinica, Inst Theoret Phys, POB 2735, Beijing 100080, Peoples R China.
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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,&Guo, HY , Acad Sinica, Inst Theoret Phys, POB 2735, Beijing 100080, Peoples R China..(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.
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