On the B-series composition theorem
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912025906511872 |
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| author | Butcher, John C. Mitsui, Taketomo Miyatake, Yuto Sato, Shun |
| author_facet | Butcher, John C. Mitsui, Taketomo Miyatake, Yuto Sato, Shun |
| contents | The B-series composition theorem has been an important topic in numerical analysis of ordinary differential equations for the past-half century. Traditional proofs of this theorem rely on labelled trees, whereas recent developments in B-series analysis favour the use of unlabelled trees. In this paper, we present a new proof of the B-series composition theorem that does not depend on labelled trees. A key challenge in this approach is accurately counting combinations related to ``pruning.'' This challenge is overcome by introducing the concept of ``assignment.'' |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08533 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the B-series composition theorem Butcher, John C. Mitsui, Taketomo Miyatake, Yuto Sato, Shun Numerical Analysis The B-series composition theorem has been an important topic in numerical analysis of ordinary differential equations for the past-half century. Traditional proofs of this theorem rely on labelled trees, whereas recent developments in B-series analysis favour the use of unlabelled trees. In this paper, we present a new proof of the B-series composition theorem that does not depend on labelled trees. A key challenge in this approach is accurately counting combinations related to ``pruning.'' This challenge is overcome by introducing the concept of ``assignment.'' |
| title | On the B-series composition theorem |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2409.08533 |