dc.contributor.author | Arnold, Martin | |
dc.contributor.author | Celledoni, Elena | |
dc.contributor.author | Cokaj, Ergys | |
dc.contributor.author | Owren, Brynjulf Rustad | |
dc.contributor.author | Tumiotto, Denise | |
dc.date.accessioned | 2024-02-13T07:52:46Z | |
dc.date.available | 2024-02-13T07:52:46Z | |
dc.date.created | 2024-01-18T16:31:03Z | |
dc.date.issued | 2024 | |
dc.identifier.issn | 2158-2505 | |
dc.identifier.uri | https://hdl.handle.net/11250/3117115 | |
dc.description.abstract | We 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.iso | eng | en_US |
dc.publisher | American Institute of Mathematical Sciences | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | B-stability of numerical integrators on Riemannian manifolds | en_US |
dc.title.alternative | B-stability of numerical integrators on Riemannian manifolds | en_US |
dc.type | Peer reviewed | en_US |
dc.type | Journal article | en_US |
dc.description.version | publishedVersion | en_US |
dc.rights.holder | Copyright © 2024 American Institute of Mathematical Sciences | en_US |
dc.source.journal | Journal of Computational Dynamics | en_US |
dc.identifier.doi | 10.3934/jcd.2024002 | |
dc.identifier.cristin | 2229785 | |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.fulltext | original | |
cristin.qualitycode | 1 | |