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dc.contributor.authorCalatayud, Julia
dc.contributor.authorCortés, Juan Carlos
dc.contributor.authorJornet, Marc
dc.date.accessioned2022-11-30T15:32:23Z
dc.date.available2022-11-30T15:32:23Z
dc.date.issued2018-11-27
dc.identifier.citationCalatayud, J., Cortés, J. C., & Jornet, 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, 23(4), 76.ca_CA
dc.identifier.issn2297-8747
dc.identifier.urihttp://hdl.handle.net/10234/201003
dc.description.abstractThe 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.ca_CA
dc.format.extent14 p.ca_CA
dc.format.mimetypeapplication/pdfca_CA
dc.language.isoengca_CA
dc.publisherMDPIca_CA
dc.relationPrograma de Ayudas de Investigación y Desarrollo (PAID)ca_CA
dc.relation.isPartOfMathematical and Computational Applications, Vol.23, Iss. 4 (December 2018)ca_CA
dc.rights© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).ca_CA
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/ca_CA
dc.subjectrandom non-autonomous second order linear differential equationca_CA
dc.subjectmean square analytic solutionca_CA
dc.subjectrandom power seriesca_CA
dc.subjectuncertainty quantificationca_CA
dc.subject34F05ca_CA
dc.subject60H10ca_CA
dc.subject60H35ca_CA
dc.subject65C20ca_CA
dc.subject65C30ca_CA
dc.titleSome Notes to Extend the Study on Random Non-Autonomous Second Order Linear Differential Equations Appearing in Mathematical Modelingca_CA
dc.typeinfo:eu-repo/semantics/articleca_CA
dc.identifier.doihttps://doi.org/10.3390/mca23040076
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessca_CA
dc.type.versioninfo:eu-repo/semantics/publishedVersionca_CA
project.funder.nameMinisterio de Economía y Competitividadca_CA
project.funder.nameUniversitat Politècnica de Valènciaca_CA
oaire.awardNumberMTM2017-89664-Pca_CA


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© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Excepto si se señala otra cosa, la licencia del ítem se describe como: © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).