On the B-series composition theorem

Butcher, John C.; Mitsui, Taketomo; Miyatake, Yuto et al.

BIT Numerical Mathematics, 2025, 65(2), 22

Number of Access:207（2025-08-15 01:10 Counts）

Identifier to cite or link to this item: https://hdl.handle.net/11094/101309

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Title
On the B-series composition theorem
Creator
CreatorName
Butcher, John C.
NRID
1000050027380 1000050027380
CreatorName
Mitsui, Taketomo
NRID
1000060757384 1000060757384
ORCID
0000-0002-5742-6251 0000-0002-5742-6251
researchmap permalink
miyatake miyatake
Scopus Author ID
41861885700 41861885700
CreatorName
Miyatake, Yuto
NRID
1000040849072 1000040849072
CreatorName
Sato, Shun
Subject
B-series
Composition
Pruning
Rooted trees
Description
This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at : https://doi.org/10.1007/s10543-025-01063-y
Abstract
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.”
Publisher
Springer Science and Business Media B.V.
Source Title
BIT Numerical Mathematics
Volume (Issue)
65(2)
Page
22
Date of Issued
2025-05-04
Language
English
Handle URL
https://hdl.handle.net/11094/101309
PISSN
00063835
eISSN
15729125
Relation.isVersionOf
DOI (Publisher Version)
https://doi.org/10.1007/s10543-025-01063-y
Access Rights
embargoed access
CopyRight
The full-text file will be made open to the public on 4 May 2026 in accordance with the publisher's policy.
oaire:version
Accepted Manuscript
Category
学術雑誌論文 Journal Article