Aromatic Butcher Series

@article{MuntheKaas2016AromaticBS,
  title={Aromatic Butcher Series},
  author={Hans Z. Munthe-Kaas and Olivier Verdier},
  journal={Foundations of Computational Mathematics},
  year={2016},
  volume={16},
  pages={183-215}
}
We show that without other further assumption than affine equivariance and locality, a numerical integrator has an expansion in a generalized form of Butcher series (B-series), which we call aromatic B-series. We obtain an explicit description of aromatic B-series in terms of elementary differentials associated to aromatic trees, which are directed graphs generalizing trees. We also define a new class of integrators, the class of aromatic Runge–Kutta methods, that extends the class of Runge… 

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