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Solving the random Legendre differential equation: Mean square power series solution and its statistical functions

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Solving the random Legendre differential equation: Mean square power series solution and its statistical functions

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dc.contributor.author Calbo Sanjuán, Gema es_ES
dc.contributor.author Cortés López, Juan Carlos es_ES
dc.contributor.author Jódar Sánchez, Lucas Antonio es_ES
dc.contributor.author Villafuerte Altuzar, Laura
dc.date.accessioned 2014-05-20T13:06:51Z
dc.date.issued 2011-05
dc.identifier.issn 0898-1221
dc.identifier.uri http://hdl.handle.net/10251/37627
dc.description.abstract In this paper we construct, by means of random power series, the solution of second order linear differential equations of Legendre-type containing uncertainty through its coefficients and initial conditions. By assuming appropriate hypotheses on the data, we prove that the constructed random power series solution is mean square convergent. In addition, the main statistical functions of the approximate solution stochastic process generated by truncation of the exact power series solution are given. Finally, we apply the proposed method to some illustrative examples to compare the numerical results for the average and the variance with respect to those obtained by the Monte Carlo approach. © 2011 Elsevier Ltd. All rights reserved. es_ES
dc.description.sponsorship This work has been partially supported by the Spanish M.C.Y.T. grants MTM2009-08587, DPI2010-20891-C02-01, Universidad Politecnica de Valencia grant PAID06-09-2588 and Mexican Conacyt. en_EN
dc.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation.ispartof Computers and Mathematics with Applications es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Mean square and mean fourth calculus es_ES
dc.subject Random differential equation es_ES
dc.subject Random power series solution es_ES
dc.subject Approximate solution es_ES
dc.subject Illustrative examples es_ES
dc.subject Initial conditions es_ES
dc.subject Legendre es_ES
dc.subject Mean square es_ES
dc.subject Monte Carlo approach es_ES
dc.subject Numerical results es_ES
dc.subject Power series es_ES
dc.subject Power series solutions es_ES
dc.subject Second order linear differential equation es_ES
dc.subject Statistical functions es_ES
dc.subject Stochastic process es_ES
dc.subject Calculations es_ES
dc.subject Differential equations es_ES
dc.subject Monte Carlo methods es_ES
dc.subject Numerical methods es_ES
dc.subject Random processes es_ES
dc.subject Differentiation (calculus) es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Solving the random Legendre differential equation: Mean square power series solution and its statistical functions es_ES
dc.type Artículo es_ES
dc.embargo.lift 10000-01-01
dc.embargo.terms forever es_ES
dc.identifier.doi 10.1016/j.camwa.2011.03.045
dc.relation.projectID info:eu-repo/grantAgreement/MICINN//MTM2009-08587/ES/Ecuaciones Diferenciales Aleatorias Y Aplicaciones/ / es_ES
dc.relation.projectID info:eu-repo/grantAgreement/UPV//PAID-06-09-2588/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MICINN//DPI2010-20891-C02-01/ES/MODELIZACION Y METODOS NUMERICOS, ALEATORIOS Y DETERMINISTAS, PARA EL FILTRADO DE PARTICULAS DIESEL EN MOTORES DE COMBUSTION INTERNA SOBREALIMENTADOS/ 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 Calbo Sanjuán, G.; Cortés López, JC.; Jódar Sánchez, LA.; Villafuerte Altuzar, L. (2011). Solving the random Legendre differential equation: Mean square power series solution and its statistical functions. Computers and Mathematics with Applications. 61(9):2782-2792. https://doi.org/10.1016/j.camwa.2011.03.045 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://dx.doi.org/10.1016/j.camwa.2011.03.045 es_ES
dc.description.upvformatpinicio 2782 es_ES
dc.description.upvformatpfin 2792 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 61 es_ES
dc.description.issue 9 es_ES
dc.relation.senia 210540
dc.contributor.funder Ministerio de Ciencia e Innovación es_ES
dc.contributor.funder Universitat Politècnica de València es_ES
dc.contributor.funder Consejo Nacional de Ciencia y Tecnología, México es_ES


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