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On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random power series solution and approximation of its statistical moments

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On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random power series solution and approximation of its statistical moments

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dc.contributor.author Calatayud-Gregori, Julia es_ES
dc.contributor.author Cortés, J.-C. es_ES
dc.contributor.author Jornet-Sanz, Marc es_ES
dc.date.accessioned 2020-05-29T03:33:06Z
dc.date.available 2020-05-29T03:33:06Z
dc.date.issued 2019-07 es_ES
dc.identifier.uri http://hdl.handle.net/10251/144575
dc.description "This is the peer reviewed version of the following article: Calatayud, J, Cortés, J-;C, Jornet, M. On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random power series solution and approximation of its statistical moments. Comp and Math Methods. 2019; 1:e1045. https://doi.org/10.1002/cmm4.1045 , which has been published in final form at https://doi.org/10.1002/cmm4.1045. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving." es_ES
dc.description.abstract [EN] In this paper, we construct two linearly independent response processes to the random Legendre differential equation on (-1,1)U(1,3), consisting of Lp(omega) convergent random power series around the regular¿singular point 1. A theorem on the existence and uniqueness of Lp(omega) solution to the random Legendre differential equation on the intervals (-1,1) and (1,3) is obtained. The hypotheses assumed are simple: initial conditions in Lp(omega) and random input A in L infinite(omega) (this is equivalent to A having absolute moments that grow at most exponentially). Thus, this paper extends the deterministic theory to a random framework. Uncertainty quantification for the solution stochastic process is performed by truncating the random series and taking limits in Lp(omega). In the numerical experiments, we approximate its expectation and variance for certain forms of the differential equation. The reliability of our approach is compared with Monte Carlo simulations and generalized polynomial chaos expansions. es_ES
dc.description.sponsorship Spanish Ministerio de Economía y Competitividad, Grant/Award Number: MTM2017-89664-P; Programa de Ayudas de Investigación y Desarrollo; Universitat Politècnica de València es_ES
dc.language Inglés es_ES
dc.publisher John Wiley & Sons es_ES
dc.relation.ispartof Computational and Mathematical Methods es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Lp random calculus es_ES
dc.subject Random Legendre differential equation es_ES
dc.subject Random power series es_ES
dc.subject Regular-singular point es_ES
dc.subject Uncertainty quantification es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random power series solution and approximation of its statistical moments es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1002/cmm4.1045 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-89664-P/ES/PROBLEMAS DINAMICOS CON INCERTIDUMBRE SIMULABLE: MODELIZACION MATEMATICA, ANALISIS, COMPUTACION Y APLICACIONES/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Calatayud-Gregori, J.; Cortés, J.; Jornet-Sanz, M. (2019). On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random power series solution and approximation of its statistical moments. Computational and Mathematical Methods. 1(4):1-12. https://doi.org/10.1002/cmm4.1045 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1002/cmm4.1045 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 12 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 1 es_ES
dc.description.issue 4 es_ES
dc.identifier.eissn 2577-7408 es_ES
dc.relation.pasarela S\387624 es_ES
dc.contributor.funder Agencia Estatal de Investigación es_ES
dc.contributor.funder Universitat Politècnica de València es_ES
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