Multi-indice B-series
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912293979160576 |
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| author | Bruned, Yvain Ebrahimi-Fard, Kurusch Hou, Yingtong |
| author_facet | Bruned, Yvain Ebrahimi-Fard, Kurusch Hou, Yingtong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13971 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multi-indice B-series Bruned, Yvain Ebrahimi-Fard, Kurusch Hou, Yingtong Numerical Analysis 60L70, 65L06, 16T05 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. |
| title | Multi-indice B-series |
| topic | Numerical Analysis 60L70, 65L06, 16T05 |
| url | https://arxiv.org/abs/2402.13971 |