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dc.contributor.authorCurry, Charles Henry Alexander
dc.contributor.authorOwren, Brynjulf
dc.date.accessioned2020-02-05T13:39:47Z
dc.date.available2020-02-05T13:39:47Z
dc.date.created2018-05-31T01:44:07Z
dc.date.issued2019
dc.identifier.citationNumerical Algorithms. 2019, 82 (4), 1359-1376.nb_NO
dc.identifier.issn1017-1398
dc.identifier.urihttp://hdl.handle.net/11250/2639869
dc.description.abstractWe introduce variable step size commutator free Lie group integrators, where the error control is achieved using embedded Runge–Kutta pairs. These are schemes for the integration of initial value problems posed on homogeneous spaces by means of Lie group actions. The focus is on commutator free methods, in which the approximation evolves by composing flows generated by Lie group exponentials. Such methods are encoded by a generalization of Butcher’s Runge–Kutta tableaux, but it is known that more order conditions must be satisfied to obtain a scheme of a given order than are required for classical RK schemes. These extra considerations complicate the task of designing embedded pairs. Moreover, whilst the computational cost of RK schemes is typically dominated by function evaluations, in most situations, the dominant cost of commutator free Lie group integrators comes from computing Lie group exponentials. We therefore give Butcher tableaux for several families of methods of order 3(2) and 4(3), designed with a view to minimizing the number of Lie group exponentials required at each time step, and briefly discuss practical error control mechanisms. The methods are then applied to a selection of examples illustrating the expected behaviour.nb_NO
dc.language.isoengnb_NO
dc.publisherSpringer Verlagnb_NO
dc.relation.urihttps://arxiv.org/abs/1804.02123
dc.titleVariable step size commutator free Lie group integratorsnb_NO
dc.typeJournal articlenb_NO
dc.typePeer reviewednb_NO
dc.description.versionacceptedVersionnb_NO
dc.subject.nsiVDP::Matematikk: 410nb_NO
dc.subject.nsiVDP::Mathematics: 410nb_NO
dc.source.pagenumber1359-1376nb_NO
dc.source.volume82nb_NO
dc.source.journalNumerical Algorithmsnb_NO
dc.source.issue4nb_NO
dc.identifier.doihttps://doi.org/10.1007/s11075-019-00659-0
dc.identifier.cristin1587881
dc.relation.projectEC/H2020/CHiPSnb_NO
dc.relation.projectNorges forskningsråd: 231632nb_NO
dc.relation.projectEC/H2020/CHIPSnb_NO
dc.description.localcodeThis is a post-peer-review, pre-copyedit version of an article. The final authenticated version is available online at: https://doi.org/10.1007/s11075-019-00659-0nb_NO
cristin.unitcode194,63,15,0
cristin.unitnameInstitutt for matematiske fag
cristin.ispublishedtrue
cristin.fulltextpostprint
cristin.qualitycode1


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