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| Phase analysis of Lie series algorithm and explicit symplectic algorithm |
| Received:June 28, 2007 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20092004 |
| KeyWord:Lie series algorithm explicit symplectic geometric algorithm phase amplitude |
| Author | Institution |
| 邢誉峰 |
北京航空航天大学 固体力学研究所,北京 |
| 冯伟 |
北京航空航天大学 固体力学研究所,北京 |
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| Abstract: |
| Taking a linear separable Hamiltonian system as an example, the phase errors of Lie series algorithms and explicit symplectic geometric algorithms were analyzed in details, the accuracy order for amplitude preserving symplectic of Lie series algorithms and its improving method were investigated, by which the amplitude accuracy is increased and but phase accuracy is effected less. There is one conclusion that the order of explicit symplectic integration algorithm is about the amplitude not about the phase, but the order of Lie series algorithms is about the amplitude and the phase simultaneously. The phase accuracy of the third order explicit symplectic method is higher than that of the fourth order explicit and implicit symplectic integration algorithms, and that of the fourth order Lie series algorithm and the fourth order modified Lie series algorithm. Moreover, the phase of an algorithm can either backward or forward comparing with the exact solution. Finally, it is concluded for Lie series algorithm that the accuracy of amplitude and phase can be improved with the increase of its order, but the conclusion is not valid for the explicit symplectic integration methods. Taking the efficiency and the accuracy into account, the three order explicit symplectic method is superior to the others for linear and nonlinear separable Hamiltonian systems. |
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