New families of symplectic splitting methods for numerical integration in dynamical astronomy

@article{Blanes2013NewFO,
  title={New families of symplectic splitting methods for numerical integration in dynamical astronomy},
  author={S. Blanes and F. Casas and A. Farr{\'e}s and J. Laskar and J. Makazaga and A. Murua},
  journal={Applied Numerical Mathematics},
  year={2013},
  volume={68},
  pages={58-72}
}
We present new splitting methods designed for the numerical integration of near-integrable Hamiltonian systems, and in particular for planetary N-body problems, when one is interested in very accurate results over a large time span. We derive in a systematic way an independent set of necessary and sufficient conditions to be satisfied by the coefficients of splitting methods to achieve a prescribed order of accuracy. Splitting methods satisfying such (generalized) order conditions are… Expand

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