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Zbl 1147.65103
Chen, Jing-Bo; Qin, Meng-Zhao; Scherer, Rudolf
Multisymplectic and variational integrators. (English)
[J] Int. J. Pure Appl. Math. 44, No. 4, 509-536 (2008). ISSN 1311-8080

Summary: Recently multisymplectic discretizations are attracting much attention, because they are the vigorous component of the structure-preserving algorithms. In this paper, the new development in the field of multisymplectic discretizations is systematically described and some very interesting new results are given. Multisymplectic and variational integrators are studied from a comparative point of view. The composition method for constructing higher order multisymplectic integrators is presented. The equivalence of variational integrators to multisymplectic integrators is proved.

MSC 2000:: *65P10 Hamiltonian systems including symplectic integrators
65M06 Finite difference methods (IVP of PDE)
65M12 Stability and convergence of numerical methods (IVP of PDE)
65M60 Finite numerical methods (IVP of PDE)
65M70 Spectral, collocation and related methods (IVP of PDE)
37M15 Symplectic integrators
37K05 Hamiltonian structures, etc.

Keywords: structure-preserving; spectral method; composition method; finite element method; Birkhoffian system

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