  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.
