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arXiv · 1308.5824

Aromatic Butcher Series

Hans Munthe-Kaas·Olivier Verdier
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Abstract

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-Kutta methods, and have aromatic B-series expansion but are not B-series methods. Finally, those results are partially extended to the case of more general affine group equivariance.

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Hans Munthe-Kaas, Olivier Verdier. 2013-08-27. Aromatic Butcher Series. https://doi.org/10.1007/s10208-015-9245-0

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