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dc.contributor.authorLaurent, Adrien Ange Andre
dc.contributor.authorMclachlan, Robert I.
dc.contributor.authorMunthe-Kaas, Hans Zanna
dc.contributor.authorVerdier, Olivier Philippe Paul
dc.date.accessioned2023-09-18T11:18:14Z
dc.date.available2023-09-18T11:18:14Z
dc.date.issued2023-08-08
dc.description.abstractAromatic B-series were introduced as an extension of standard Butcher-series for the study of volume-preserving integrators. It was proven with their help that the only volume-preserving B-series method is the exact flow of the differential equation. The question was raised whether there exists a volume-preserving integrator that can be expanded as an aromatic B-series. In this work, we introduce a new algebraic tool, called the aromatic bicomplex, similar to the variational bicomplex in variational calculus. We prove the exactness of this bicomplex and use it to describe explicitly the key object in the study of volume-preserving integrators: the aromatic forms of vanishing divergence. The analysis provides us with a handful of new tools to study aromatic B-series, gives insights on the process of integration by parts of trees, and allows to describe explicitly the aromatic B-series of a volumepreserving integrator. In particular, we conclude that an aromatic Runge–Kutta method cannot preserve volume.en_US
dc.identifier.citationLaurent, Mclachlan, Munthe-Kaas, Verdier. The aromatic bicomplex for the description of divergence-free aromatic forms and volume-preserving integrators. Forum of Mathematics, Sigma. 2023;11en_US
dc.identifier.cristinIDFRIDAID 2174240
dc.identifier.doi10.1017/fms.2023.63
dc.identifier.issn2050-5094
dc.identifier.urihttps://hdl.handle.net/10037/31063
dc.language.isoengen_US
dc.publisherCambridge University Pressen_US
dc.relation.journalForum of Mathematics, Sigma
dc.rights.accessRightsopenAccessen_US
dc.rights.holderCopyright 2023 The Author(s)en_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0en_US
dc.rightsAttribution 4.0 International (CC BY 4.0)en_US
dc.titleThe aromatic bicomplex for the description of divergence-free aromatic forms and volume-preserving integratorsen_US
dc.type.versionpublishedVersionen_US
dc.typeJournal articleen_US
dc.typeTidsskriftartikkelen_US
dc.typePeer revieweden_US


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Attribution 4.0 International (CC BY 4.0)
Except where otherwise noted, this item's license is described as Attribution 4.0 International (CC BY 4.0)