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Bibliographic Details
Main Authors: Butcher, John C., Mitsui, Taketomo, Miyatake, Yuto, Sato, Shun
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2409.08533
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Table of 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.''