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Some notes to extend the study on random non-autonomous second order linear differential equations appearing in Mathematical Modeling

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Some notes to extend the study on random non-autonomous second order linear differential equations appearing in Mathematical Modeling

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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 2019-09-07T20:02:02Z
dc.date.available 2019-09-07T20:02:02Z
dc.date.issued 2018 es_ES
dc.identifier.uri http://hdl.handle.net/10251/125216
dc.description.abstract [EN] The objective of this paper is to complete certain issues from our recent contribution (Calatayud, J.; Cortés, J.-C.; Jornet, M.; Villafuerte, L. Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties. Adv. Differ. Equ. 2018, 392, 1¿29, doi:10.1186/s13662-018-1848-8). We restate the main theorem therein that deals with the homogeneous case, so that the hypotheses are clearer and also easier to check in applications. Another novelty is that we tackle the non-homogeneous equation with a theorem of existence of mean square analytic solution and a numerical example. We also prove the uniqueness of mean square solution via a habitual Lipschitz condition that extends the classical Picard theorem to mean square calculus. In this manner, the study on general random non-autonomous second order linear differential equations with analytic data processes is completely resolved. Finally, we relate our exposition based on random power series with polynomial chaos expansions and the random differential transform method, the latter being a reformulation of our random Fröbenius method. es_ES
dc.description.sponsorship This work has been supported by the Spanish Ministerio de Economía y Competitividad Grant MTM2017-89664-P. The author Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigación y Desarrollo (PAID), Universitat Politècnica de València.
dc.language Inglés es_ES
dc.publisher MDPI AG es_ES
dc.relation.ispartof Mathematical and Computational Applications (Online) es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject Random non-autonomous second order linear differential equation es_ES
dc.subject Mean square analytic solution es_ES
dc.subject Random power series es_ES
dc.subject Uncertainty quantification es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Some notes to extend the study on random non-autonomous second order linear differential equations appearing in Mathematical Modeling es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.3390/mca23040076 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. (2018). Some notes to extend the study on random non-autonomous second order linear differential equations appearing in Mathematical Modeling. Mathematical and Computational Applications (Online). 23(4):1-14. https://doi.org/10.3390/mca23040076 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://doi.org/10.3390/mca23040076 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 14 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 23 es_ES
dc.description.issue 4 es_ES
dc.identifier.eissn 2297-8747 es_ES
dc.relation.pasarela S\373056 es_ES
dc.contributor.funder Agencia Estatal de Investigación es_ES


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