Abstract
In this paper, the classical and pre-Lie Magnus expansions have been studied, discussing how one can find a recursion for the pre-Lie case which already incorporates the pre-Lie identity. A combinatorial vision of a numerical method proposed by S. Blanes, F. Casas, and J. Ros in [4], has been given on a writing of the classical Magnus expansion in a free Lie algebra, using a pre-Lie structure.
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