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

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.contributor.authorChartier, P.
dc.contributor.authorMurua, A.
dc.contributor.authorSanz Serna, Jesús María
dc.contributor.funderMinisterio de Ciencia e Innovación (España)es
dc.date.accessioned2021-04-30T09:48:42Z
dc.date.available2021-04-30T09:48:42Z
dc.date.issued2015-04-01
dc.description.abstractIn 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.en
dc.description.sponsorshipA. 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.en
dc.description.statusPublicadoes
dc.format.extent21
dc.identifier.bibliographicCitationFoundations of Computational Mathematics, (2015), v. 15, p.: 591–612..en
dc.identifier.doihttps://doi.org/10.1007/s10208-013-9175-7
dc.identifier.issn1615-3375
dc.identifier.publicationfirstpage591
dc.identifier.publicationlastpage612
dc.identifier.publicationtitleFOUNDATIONS OF COMPUTATIONAL MATHEMATICSen
dc.identifier.publicationvolume15
dc.identifier.urihttps://hdl.handle.net/10016/32515
dc.identifier.uxxiAR/0000020038
dc.language.isoengen
dc.publisherSpringeres
dc.relation.projectIDGobierno de España. MTM2010-18246-C03-03es
dc.relation.projectIDGobierno de España. MTM2010-18246-C03-01es
dc.rights© SFoCM 2013en
dc.rights.accessRightsopen accesses
dc.subject.ecienciaMatemáticases
dc.subject.otherAveragingen
dc.subject.otherHigh-order averagingen
dc.subject.otherQuasi-stroboscopic averagingen
dc.subject.otherHighly oscillatory problemsen
dc.subject.otherHamiltonian problemsen
dc.subject.otherFormal seriesen
dc.subject.otherFirst integralsen
dc.subject.otherNear-integrable systemsen
dc.titleHigher-order averaging, formal series and numerical integration III: error boundsen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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