On pre-Lie Magnus expansion

TL;DR

This paper explores the pre-Lie Magnus expansion, providing a recursive approach that integrates the pre-Lie identity and offers a combinatorial perspective on numerical methods related to classical Magnus expansion.

Contribution

It introduces a recursive formulation for the pre-Lie Magnus expansion that naturally incorporates the pre-Lie identity and connects it with combinatorial methods.

Findings

Develops a recursion for the pre-Lie Magnus expansion.

Provides a combinatorial interpretation of a numerical method.

Links classical and pre-Lie Magnus expansions through algebraic structures.

Abstract

In this paper, we study the classical and pre-Lie Magnus expansions, discussing how we can find a recursion for the pre-Lie case which already incorporates the pre-Lie identity. We give a combinatorial vision of a numerical method proposed by S. Blanes, F. Casas, and J. Ros, on a writing of the classical Magnus expansion in a free Lie algebra, using a pre-Lie structure.