Pré-Publication, Document De Travail Année : 2026

The free tracial post-Lie-Rinehart algebra of planar aromatic trees for the design of divergence-free Lie-group methods

Résumé

Aromatic Butcher series were successfully introduced for the study and design of numeri- cal integrators that preserve volume while solving differential equations in Euclidean spaces. They are naturally associated to pre-Lie-Rinehart algebras and pre-Hopf algebroids struc- tures, and aromatic trees were shown to form the free tracial pre-Lie-Rinehart algebra. In this paper, we present the generalisation of aromatic trees for the study of divergence-free integrators on manifolds. We introduce planar aromatic trees, show that they span the free tracial post-Lie-Rinehart algebra, and apply them for deriving new Lie-group methods that preserve geometric divergence-free features up to a high order of accuracy.

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hal-05575534 , version 1 (01-04-2026)

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  • HAL Id : hal-05575534 , version 1

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Adrien Busnot Laurent, Hans Munthe-Kaas, Venkatesh G. S.. The free tracial post-Lie-Rinehart algebra of planar aromatic trees for the design of divergence-free Lie-group methods. 2026. ⟨hal-05575534⟩
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