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Multisymplectic and variational integrators. (English) Zbl 1147.65103
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:
65P10Numerical methods for Hamiltonian systems including symplectic integrators
65M06Finite difference methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
65M70Spectral, collocation and related methods (IVP of PDE)
37M15Symplectic integrators (dynamical systems)
37K05Hamiltonian structures, symmetries, variational principles, conservation laws