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arXiv · 2402.13971

Multi-indice B-series

Yvain Bruned·Kurusch Ebrahimi-Fard·Yingtong Hou
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Abstract

We propose a novel way to study numerical methods for ordinary differential equations in one dimension 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. Furthermore, such multi-indices B-series uniquely characterize the Taylor expansion of one-dimensional local and affine equivariant maps.

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Yvain Bruned, Kurusch Ebrahimi-Fard, Yingtong Hou. 2024-11-17. Multi-indice B-series. https://doi.org/10.1112/jlms.70049

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