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Guo, HY; Li, YQ; Wu, K; Wang, SK; Guo, HY , Acad Sinica, Inst Theoret Phys, POB 2735, Beijing 100080, Peoples R China.
Difference discrete variational principles, Euler-Lagrange cohomology and symplectic, multisymplectic structures III: Application to symplectic and multisymplectic algorithms
Source PublicationCOMMUNICATIONS IN THEORETICAL PHYSICS
AbstractIn 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.
2002
ISSN0253-6102
Volume37Issue:3Pages:257-264
Subject AreaPhysics
Indexed BySCI
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Document Type期刊论文
Identifierhttp://ir.itp.ac.cn/handle/311006/13565
Collection理论物理所科研产出_SCI论文
Corresponding AuthorGuo, HY , Acad Sinica, Inst Theoret Phys, POB 2735, Beijing 100080, Peoples R China.
Recommended Citation
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,&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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