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dc.creatorFerreira González, Cheloes_ES
dc.creatorLópez García, José Luises_ES
dc.creatorPérez Sinusía, Esteres_ES
dc.identifier.issn0176-4276 (Print)
dc.identifier.issn1432-0940 (Electronic)
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:
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.publisherSpringer USen
dc.relation.ispartofConstructive Approximation (2016) 43:273–290en
dc.rights© Springer Science+Business Media New York 2015en
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.typeArtículo / Artikuluaes
dc.contributor.departmentIngeniería Matemática e Informáticaes_ES
dc.contributor.departmentMatematika eta Informatika Ingeniaritzaeu
dc.rights.accessRightsAcceso abierto / Sarbide irekiaes
dc.type.versionVersión aceptada / Onetsi den bertsioaes

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