Symplectic integrators with adaptive time steps

@article{Richardson2012SymplecticIW,
  title={Symplectic integrators with adaptive time steps},
  author={A. Stephen Richardson and John M. Finn},
  journal={Plasma Physics and Controlled Fusion},
  year={2012},
  volume={54},
  pages={014004}
}
In recent decades, there have been many attempts to construct symplectic integrators with variable time steps, with rather disappointing results. In this paper, we identify the causes for this lack of performance, and find that they fall into two categories. In the first, the time step is considered a function of time alone, ? = ?(t). In this case, backward error analysis shows that while the algorithms remain symplectic, parametric instabilities may arise because of resonance between… 

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