Multi-indice B-series
<|reference_start|>Multi-indice B-series: We propose a novel way to describe numerical methods for ordinary differential equations via the notion of multi-indice. The main idea is to replace rooted trees in Butcher's B-series by multi-indices. The latter were introduced recently in the context of describing solutions of singular stochastic partial differential equations. The combinatorial shift away from rooted trees allows for a compressed description of numerical schemes. Moreover, these multi-indices B-series characterise uniquely the Taylor development of local and affine equivariant maps.<|reference_end|>
@article{bruned2024multi-indice,
    title={Multi-indice B-series},
    author={Yvain Bruned, Kurusch Ebrahimi-Fard, Yingtong Hou},
    journal={arXiv preprint arXiv:2402.13971},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.13971},
    primaryClass={math.NA cs.NA}
}