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Exact evolution of time-reversible symplectic integrators and their phase error for the harmonic oscillator

Siu A. Chin·Sante R. Scuro
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Abstract

The evolution of any factorized time-reversible symplectic integrators, when applied to the harmonic oscillator, can be exactly solved in a closed form. The resulting modified Hamiltonians demonstrate the convergence of the Lie series expansions. They are also less distorted than modified Hamiltonian of non-reversible algorithms. The analytical form for the modified angular frequency can be used to assess the phase error of any time-reversible algorithm.

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Siu A. Chin, Sante R. Scuro. 2004-11-19. Exact evolution of time-reversible symplectic integrators and their phase error for the harmonic oscillator. https://doi.org/10.1016/j.physleta.2005.05.062

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