Convergent and asymptotic methods for second-order difference equations with a large parameter

Ferreira González, Chelo; López García, José Luis; Pérez Sinusía, Ester

Publication:
Convergent and asymptotic methods for second-order difference equations with a large parameter

dc.contributor.author	Ferreira González, Chelo
dc.contributor.author	López García, José Luis
dc.contributor.author	Pérez Sinusía, Ester
dc.contributor.department	Matematika eta Informatika Ingeniaritza	eu
dc.contributor.department	Institute for Advanced Materials and Mathematics - INAMAT2	en
dc.contributor.department	Ingeniería Matemática e Informática	es_ES
dc.contributor.funder	Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa	es
dc.date.accessioned	2018-12-14T12:04:18Z
dc.date.available	2019-11-08T00:00:17Z
dc.date.issued	2018
dc.description	This is a post-peer-review, pre-copyedit version of an article published in Mediterranean Journal of Mathematics. The final authenticated version is available online at: https://doi.org/10.1007/s00009-018-1267-9	en
dc.description.abstract	We consider the second-order linear difference equation y(n+2)−2ay(n+1)−Λ2y(n)=g(n)y(n)+f(n)y(n+1) , where Λ is a large complex parameter, a≥0 and g and f are sequences of complex numbers. Two methods are proposed to find the asymptotic behavior for large \|Λ\|of the solutions of this equation: (i) an iterative method based on a fixed point method and (ii) a discrete version of Olver’s method for second-order linear differential equations. Both methods provide an asymptotic expansion of every solution of this equation. The expansion given by the first method is also convergent and may be applied to nonlinear problems. Bounds for the remainders are also given. We illustrate the accuracy of both methods for the modified Bessel functions and the associated Legendre functions of the first kind.	en
dc.description.sponsorship	This research was supported by the Spanish Ministry of Economía y Competitividad, project MTM2014-52859-P. The Universidad Pública de Navarra is acknowledged by its financial support.	en
dc.embargo.lift	2019-11-08
dc.embargo.terms	2019-11-08
dc.format.extent	16 p.
dc.format.mimetype	application/pdf	en
dc.identifier.doi	10.1007/s00009-018-1267-9
dc.identifier.issn	1660-5446 (Print)
dc.identifier.issn	1660-5454 (Electronic)
dc.identifier.uri	https://academica-e.unavarra.es/handle/2454/31783
dc.language.iso	eng	en
dc.publisher	Springer	en
dc.relation.ispartof	Mediterranean Journal of Mathematics (2018) 15:224	en
dc.relation.projectID	info:eu-repo/grantAgreement/MINECO//MTM2014-52859-P/ES/	en
dc.relation.publisherversion	https://doi.org/10.1007/s00009-018-1267-9
dc.rights	© Springer Nature Switzerland AG 2018	en
dc.rights.accessRights	info:eu-repo/semantics/openAccess	en
dc.rights.accessRights	Acceso abierto / Sarbide irekia	es
dc.subject	Second-order difference equations	en
dc.subject	Asymptotic expansions	en
dc.subject	Green’s functions	en
dc.subject	Olver’s method	en
dc.title	Convergent and asymptotic methods for second-order difference equations with a large parameter	en
dc.type	info:eu-repo/semantics/article
dc.type.version	info:eu-repo/semantics/acceptedVersion	en
dc.type.version	Versión aceptada / Onetsi den bertsioa	es
dspace.entity.type	Publication
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