On the B-series composition theorem
Numerical Analysis
2024-09-16 v1 Numerical Analysis
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.''
Cite
@article{arxiv.2409.08533,
title = {On the B-series composition theorem},
author = {John C. Butcher and Taketomo Mitsui and Yuto Miyatake and Shun Sato},
journal= {arXiv preprint arXiv:2409.08533},
year = {2024}
}