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dc.contributor.authorArnold, Martin
dc.contributor.authorCelledoni, Elena
dc.contributor.authorCokaj, Ergys
dc.contributor.authorOwren, Brynjulf Rustad
dc.contributor.authorTumiotto, Denise
dc.date.accessioned2024-02-13T07:52:46Z
dc.date.available2024-02-13T07:52:46Z
dc.date.created2024-01-18T16:31:03Z
dc.date.issued2024
dc.identifier.issn2158-2505
dc.identifier.urihttps://hdl.handle.net/11250/3117115
dc.description.abstractWe propose a generalization of nonlinear stability of numerical one-step integrators to Riemannian manifolds in the spirit of Butcher's notion of B-stability. Taking inspiration from Simpson-Porco and Bullo, we introduce non-expansive systems on such manifolds and define B-stability of integrators. In this first exposition, we provide concrete results for a geodesic version of the Implicit Euler (GIE) scheme. We prove that the GIE method is B-stable on Riemannian manifolds with non-positive sectional curvature. We show through numerical examples that the GIE method is expansive when applied to a certain non-expansive vector field on the 2-sphere, and that the GIE method does not necessarily possess a unique solution for large enough step sizes. Finally, we derive a new improved global error estimate for general Lie group integrators.en_US
dc.language.isoengen_US
dc.publisherAmerican Institute of Mathematical Sciencesen_US
dc.rightsNavngivelse 4.0 Internasjonal*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/deed.no*
dc.titleB-stability of numerical integrators on Riemannian manifoldsen_US
dc.title.alternativeB-stability of numerical integrators on Riemannian manifoldsen_US
dc.typePeer revieweden_US
dc.typeJournal articleen_US
dc.description.versionpublishedVersionen_US
dc.rights.holderCopyright © 2024 American Institute of Mathematical Sciencesen_US
dc.source.journalJournal of Computational Dynamicsen_US
dc.identifier.doi10.3934/jcd.2024002
dc.identifier.cristin2229785
cristin.ispublishedtrue
cristin.fulltextoriginal
cristin.fulltextoriginal
cristin.qualitycode1


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Navngivelse 4.0 Internasjonal
Except where otherwise noted, this item's license is described as Navngivelse 4.0 Internasjonal