dc.contributor.author | Eidnes, Sølve | |
dc.date.accessioned | 2022-05-11T07:23:25Z | |
dc.date.available | 2022-05-11T07:23:25Z | |
dc.date.created | 2022-02-08T08:55:53Z | |
dc.date.issued | 2022 | |
dc.identifier.citation | BIT Numerical Mathematics. 2022. | en_US |
dc.identifier.issn | 0006-3835 | |
dc.identifier.uri | https://hdl.handle.net/11250/2995162 | |
dc.description.abstract | The discrete gradient methods are integrators designed to preserve invariants of ordinary differential equations. From a formal series expansion of a subclass of these methods, we derive conditions for arbitrarily high order. We derive specific results for the average vector field discrete gradient, from which we get P-series methods in the general case, and B-series methods for canonical Hamiltonian systems. Higher order schemes are presented, and their applications are demonstrated on the Hénon–Heiles system and a Lotka–Volterra system, and on both the training and integration of a pendulum system learned from data by a neural network. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Springer | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | Order theory for discrete gradient methods | en_US |
dc.type | Peer reviewed | en_US |
dc.type | Journal article | en_US |
dc.description.version | publishedVersion | en_US |
dc.rights.holder | © The Author(s) 2022 | en_US |
dc.subject.nsi | VDP::Matematisk modellering og numeriske metoder: 427 | en_US |
dc.subject.nsi | VDP::Mathematic modelling and numerical methods: 427 | en_US |
dc.subject.nsi | Geometric integration | en_US |
dc.subject.nsi | Energy preservation | en_US |
dc.subject.nsi | B-series | en_US |
dc.subject.nsi | Neural networks | en_US |
dc.subject.nsi | Order of accuracy | en_US |
dc.subject.nsi | High-order methods | en_US |
dc.source.journal | BIT Numerical Mathematics | en_US |
dc.identifier.doi | 10.1007/s10543-022-00909-z | |
dc.identifier.cristin | 1998859 | |
dc.relation.project | Norges forskningsråd: 231632 | en_US |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 2 | |