G. Benettin and A. Giorgilli. On the Hamiltonian interpolation of near-tothe identity symplectic mappings with application to symplectic integration algorithms. J. Stat. Phys., 74(5/6):1117--1143, 1994. Home/Search Document Not in Database Summary Related Articles Check |
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Approximate Momentum Conservation for Spatial.. - Oliver, West, Wulff (2002) (Correct)
....di erential equations. In particular, Hamiltonian ordinary di erential equations can be solved by so called symplectic or variational integrators [9, 17, 28] In addition to exactly preserving the symplectic form, these integrators have been shown to conserve energy over exponentially long times [1, 7, 8, 26]. Such conservation properties are of crucial importance in celestial mechanics, molecular dynamics, and other application areas. As a continuous system and its discretization will generally diverge arbitrarily far from each other as time advances, results on approximate energy conservation for ....
....analytic autonomous Hamiltonian ODE and let t be the ow of an h dependent autonomous Hamiltonian vector eld with Hamiltonian H h approximating the dynamics of the one step method. Then we have k h (U 0 ) h (U 0 )k 36 K 1 exp( K 2 =h) for U 0 in some bounded domain S of phase space [21, 1, 8]. For the Hamiltonian H h of the Hamiltonian ow t we obtain jH h ( h (U 0 ) H h ( h (U 0 ) j = K 3 exp( K 2 =h) for U 0 2 S. Thus H h is conserved over exponentially long times provided the iterates of h (U 0 ) and the modi ed solution h (U 0 ) stay in S. We expect that the ....
G. Benettin and A. Giorgilli. On the Hamiltonian interpolation of near-to-theidentity symplectic mappings with application to symplectic integration algorithms. J. Statist. Phys. 74: 1117-1143, 1994.
Reversible Adaptive Regularization I: Perturbed Kepler Motion.. - Leimkuhler (1997) (3 citations) (Correct)
....small timesteps or nonphysical corrective measures such as rescaling of velocities are sometimes needed to maintain roughly constant energy throughout a long simulation. While preservation of symplectic structure is known to lead to improved conservation of energy in long term simulations [34, 15, 3], we show that, at least in two body scattering, discrete conservation of the symmetry and time reversal symmetry implies an orbital axial symmetry which again confers superior energy conservation. Although this result is restricted to the two body case, our numerical experiments suggest that the ....
.... Runge Kutta method by appealing to the theory of trees [15, 34] in which case the precise form of the individual terms can be described ( elementary Hamiltonians ) Still more generally, such a series can be shown to exist for any symplectic map which is a smooth perturbation of the identity [24, 3]. Fixing any finite number of terms, it is straightforward to show that each finite higher order term (involving Deltat k , k 1) of the modified equations includes a reciprocal power of q and hence vanishes as q 1, but this is not quite the whole story, since the series expansion does not ....
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G. Benettin and A. Giorgilli, On the Hamiltonian interpolation of near-to-theidentity symplectic mappings with application to symplectic integration algorithms, J. Statist. Phys. 74, 1117, 1994.
A Priori Estimates for the Global Error Committed by Runge-Kutta.. - Niesen (2001) (Correct)
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G. Benettin and A. Giorgilli. On the Hamiltonian interpolation of near-tothe identity symplectic mappings with application to symplectic integration algorithms. J. Stat. Phys., 74(5/6):1117--1143, 1994.
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