Forward Symplectic Integrators and the Long Time Phase Error in Periodic Motions

Details Forward Symplectic Integrators and the Long Time Phase Error in Periodic Motions Forward Symplectic Integrators and the Long Time Phase Error in Periodic Motions

2004-11-30

arxiv.org/abs/math-ph/0411086v3

Phys.Rev. E71 (2005) 056703

Physics

Mathematical Physics

Submitted to Phys. Rev. E, 29 Pages

Scientific paper

10.1103/PhysRevE.71.056703

We show that when time-reversible symplectic algorithms are used to solve periodic motions, the energy error after one period is generally two orders higher than that of the algorithm. By use of correctable algorithms, we show that the phase error can also be eliminated two orders higher than that of the integrator. The use of fourth order forward time step integrators can result in sixth order accuracy for the phase error and eighth accuracy in the periodic energy. We study the 1-D harmonic oscillator and the 2-D Kepler problem in great details, and compare the effectiveness of some recent fourth order algorithms.

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