Higher-Order Averaging, Formal Series and Numerical Integration I: B-series

@article{Chartier2010HigherOrderAF,
  title={Higher-Order Averaging, Formal Series and Numerical Integration I: B-series},
  author={Philippe Chartier and Ander Murua and Jes{\'u}s Mar{\'i}a Sanz Serna},
  journal={Foundations of Computational Mathematics},
  year={2010},
  volume={10},
  pages={695-727}
}
We show how B-series may be used to derive in a systematic way the analytical expressions of the high-order stroboscopic averaged equations that approximate the slow dynamics of highly oscillatory systems. For first order systems we give explicitly the form of the averaged systems with O(2) errors, j = 1, 2, 3, (2π2 denotes the period of the fast oscillations). For second order systems with large, O(2−1) forces, we give the explicit form of the averaged systems with O(2) errors, j = 1, 2. A… CONTINUE READING
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Ch

  • E. Hairer
  • Lubich and G. Wanner, Geometric Numerical…
  • 2006
Highly Influential
10 Excerpts

Modulated Fourier expansions and heterogeneous multiscale methods

  • J. M. Sanz-Serna
  • IMA J. Numer. Anal. 29
  • 2009
Highly Influential
4 Excerpts

Stabilizing with a hammer

  • J. M. Sanz-Serna
  • Stoch. Dyn. 8
  • 2008
1 Excerpt

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