Algebraic structure of aromatic B-series
Geir Bogfjellmo
TL;DR
This paper explores the algebraic properties of aromatic B-series, extending the classical B-series framework by deriving combinatorial formulas for their composition and substitution laws.
Contribution
It introduces new combinatorial formulas for the composition and substitution of aromatic B-series, broadening the algebraic understanding of these generalized series.
Findings
Derived combinatorial formulas for aromatic B-series operations
Extended B-series algebraic framework to aromatic B-series
Enhanced tools for analyzing numerical methods using aromatic B-series
Abstract
Aromatic B-series are a generalization of B-series. Some of the operations defined for B-series can be defined analogically for aromatic B-series. This paper derives combinatorial formulas for the composition and substitution laws for aromatic B-series.
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