## Abstract Optimal symplectic integrators were proposed to improve the accuracy in numerical solution of timeβdomain Maxwell's equations. The proposed symplectic scheme has almost the same stability and numerical dispersion as the mostly used fourthβorder symplectic scheme, but acquires more effic
The role of symplectic integrators in optimal control
β Scribed by Monique Chyba; Ernst Hairer; Gilles Vilmart
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 412 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0143-2087
- DOI
- 10.1002/oca.855
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π SIMILAR VOLUMES
In this article we observe that generally symplectic integrators conserve angular momentum exactly, whereas nonsymplectic integrators do not. We show that this observation extends to multiple timesteps and to constrained dynamics. Both of these devices are important for efficient molecular dynamics
In this paper the numerical integration of integrable Hamiltonian systems is considered. Symplectic one-step methods are used. The discrete system is shown to be integrable up to a remainder which is exponentially small with respect to the step size of the one-step method. As a consequence it is sho
We consider a dissipative perturbation of an integrable Hamiltonian system. The perturbed system is assumed to admit a weakly attractive invariant torus. The system is integrated with a symplectic integrator. The discrete system also admits an attractive invariant torus for sufficiently small step-s
Let Sp β«ήβ¬ be the symplectic group on a hyperbolic module V of even rank n n Ε½ . over the rational integers β«.ήβ¬ If n ) 2 then any element of Sp β«ήβ¬ is a product of n Ε½ . finite number of involutions on V, and Sp β«ήβ¬ is generated by two elements of n small order, one of which is an involution.