Higher-order averaging, formal series and numerical integration III: error bounds

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dc.contributor.author Chartier, P.
dc.contributor.author Murua, A.
dc.contributor.author Sanz Serna, Jesús María
dc.date.accessioned 2021-04-30T09:48:42Z
dc.date.available 2021-04-30T09:48:42Z
dc.date.issued 2015-04-01
dc.identifier.bibliographicCitation Foundations of Computational Mathematics, (2015), v. 15, p.: 591–612..
dc.identifier.issn 1615-3375
dc.identifier.uri http://hdl.handle.net/10016/32515
dc.description.abstract In earlier papers, it has been shown how formal series like those used nowadays to investigate the properties of numerical integrators may be used to construct high-order averaged systems or formal first integrals of Hamiltonian problems. With the new approach the averaged system (or the formal first integral) may be written down immediately in terms of (i) suitable basis functions and (ii) scalar coefficients that are computed via simple recursions. Here we show how the coefficients/basis functions approach may be used advantageously to derive exponentially small error bounds for averaged systems and approximate first integrals.
dc.description.sponsorship A. Murua and J.M. Sanz-Serna have been supported by projects MTM2010-18246-C03-03 and MTM2010-18246-C03-01 respectively from Ministerio de Ciencia e Innovación.
dc.format.extent 21
dc.language.iso eng
dc.publisher Springer
dc.rights © SFoCM 2013
dc.subject.other Averaging
dc.subject.other High-order averaging
dc.subject.other Quasi-stroboscopic averaging
dc.subject.other Highly oscillatory problems
dc.subject.other Hamiltonian problems
dc.subject.other Formal series
dc.subject.other First integrals
dc.subject.other Near-integrable systems
dc.title Higher-order averaging, formal series and numerical integration III: error bounds
dc.type article
dc.description.status Publicado
dc.subject.eciencia Matemáticas
dc.identifier.doi https://doi.org/10.1007/s10208-013-9175-7
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2010-18246-C03-03
dc.relation.projectID Gobierno de España. MTM2010-18246-C03-01
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 591
dc.identifier.publicationlastpage 612
dc.identifier.publicationvolume 15
dc.identifier.uxxi AR/0000020038
dc.contributor.funder Ministerio de Ciencia e Innovación (España)
dc.affiliation.dpto UC3M. Departamento de Matemáticas
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