学術雑誌論文

学術雑誌論文

text

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

On the B-series composition theorem

Springer Science and Business Media B.V.

英語

text

2025-05-04

https://doi.org/10.1007/s10543-025-01063-y

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

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.”

The full-text file will be made open to the public on 4 May 2026 in accordance with the publisher's policy.

101309

On the B-series composition theorem

Springer Science and Business Media B.V.

英語

2025-05-04

BIT Numerical Mathematics

65

2

22

https://doi.org/10.1007/s10543-025-01063-y

https://hdl.handle.net/11094/101309