B-series and Order Conditions for Exponential Integrators

@article{Berland2005BseriesAO,
  title={B-series and Order Conditions for Exponential Integrators},
  author={H{\aa}vard Berland and Brynjulf Owren and B{\aa}rd Skaflestad},
  journal={SIAM J. Numer. Anal.},
  year={2005},
  volume={43},
  pages={1715-1727}
}
We introduce a general format of numerical ODE-solvers which include many of the recently proposed exponential integrators. We derive a general order theory for these schemes in terms of $B$-series and bicolored rooted trees. To ease the construction of specific schemes we generalize an idea of Zennaro [{\em {Math. Comp.,}} 46 (1986), pp. 119--133] and define natural continuous extensions in the context of exponential integrators. This leads to a relatively easy derivation of some of the most… 

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