On a modifcation of Olver's method: a special case

dc.contributor.authorFerreira González, Chelo
dc.contributor.authorLópez García, José Luis
dc.contributor.authorPérez Sinusía, Ester
dc.contributor.departmentIngeniería Matemática e Informáticaes_ES
dc.contributor.departmentMatematika eta Informatika Ingeniaritzaeu
dc.date.accessioned2018-12-14T12:04:12Z
dc.date.available2018-12-14T12:04:12Z
dc.date.issued2016
dc.descriptionThis is a post-peer-review, pre-copyedit version of an article published in Constructive Approximation. The final authenticated version is available online at: https://doi.org/10.1007/s00365-015-9298-yen
dc.description.abstractWe consider the asymptotic method designed by Olver (Asymptotics and special functions. Academic Press, New York, 1974) for linear differential equations of the second order containing a large (asymptotic) parameter : xm y −2 y = g(x)y, with m ∈ Z and g continuous. Olver studies in detail the cases m = 2, especially the cases m = 0, ±1, giving the Poincaré-type asymptotic expansions of two independent solutions of the equation. The case m = 2 is different, as the behavior of the solutions for large is not of exponential type, but of power type. In this case, Olver’s theory does not give many details. We consider here the special case m = 2. We propose two different techniques to handle the problem: (1) a modification of Olver’s method that replaces the role of the exponential approximations by power approximations, and (2) the transformation of the differential problem into a fixed point problem from which we construct an asymptotic sequence of functions that converges to the unique solution of the problem. Moreover, we show that this second technique may also be applied to nonlinear differential equations with a large parameter.en
dc.description.sponsorshipThe Dirección General de Ciencia y Tecnología (REF.MTM2014-52859) is acknowledged for its financial support.en
dc.format.extent18 p.
dc.format.mimetypeapplication/pdfen
dc.identifier.doi10.1007/s00365-015-9298-y
dc.identifier.issn0176-4276 (Print)
dc.identifier.issn1432-0940 (Electronic)
dc.identifier.urihttps://academica-e.unavarra.es/handle/2454/31770
dc.language.isoengen
dc.publisherSpringer USen
dc.relation.ispartofConstructive Approximation (2016) 43:273–290en
dc.relation.projectIDinfo:eu-repo/grantAgreement/MINECO//MTM2014-52859-P/ES/
dc.relation.publisherversionhttps://doi.org/10.1007/s00365-015-9298-y
dc.rights© Springer Science+Business Media New York 2015en
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.subjectSecond-order differential equationsen
dc.subjectAsymptotic expansionsen
dc.subjectGreen’s functionsen
dc.subjectBanach’s fixed point theoremen
dc.titleOn a modifcation of Olver's method: a special caseen
dc.typeinfo:eu-repo/semantics/article
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
dspace.entity.typePublication
relation.isAuthorOfPublication8b28fd50-66f4-431e-a219-43d8c02bb077
relation.isAuthorOfPublicatione6cd33c5-6d5e-455c-b8da-32a9702e16c8
relation.isAuthorOfPublication93f891c7-529d-4972-8759-9d943c60949c
relation.isAuthorOfPublication.latestForDiscovery8b28fd50-66f4-431e-a219-43d8c02bb077

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