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Probabilistic analysis of a foundational class of generalized second-order linear differential equations in Classic Mechanics

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Probabilistic analysis of a foundational class of generalized second-order linear differential equations in Classic Mechanics

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dc.contributor.author Burgos-Simon, Clara es_ES
dc.contributor.author Cortés, J.-C. es_ES
dc.contributor.author López-Navarro, Elena es_ES
dc.contributor.author Pinto, C. M. A. es_ES
dc.contributor.author Villanueva Micó, Rafael Jacinto es_ES
dc.date.accessioned 2023-02-03T19:01:04Z
dc.date.available 2023-02-03T19:01:04Z
dc.date.issued 2022-05-05 es_ES
dc.identifier.uri http://hdl.handle.net/10251/191615
dc.description.abstract [EN] A number of relevant models in Classical Mechanics are formulated by means of the differential equation y ''(t) + At-beta y(t) = 0. In this paper, we improve the results recently established for a randomized reformulation of this model that includes a generalized derivative. The stochastic analysis permits solving that generalized model by computing reliable approximations of the probability density function of the solution, which is a stochastic process. The approach avoids constructing these approximations from limited statistical punctual information and the Principle of Maximum Entropy by directly constructing a sequence of approximations using the Probabilistic Transformation Method. We prove that these approximations converge to the exact density under mild conditions on the data. Finally, several numerical examples illustrate our theoretical findings. es_ES
dc.description.sponsorship This paper has been supported by the grant PID2020-115270GB-I00 funded by MCIN/AEI/10.13039/501100011033 and by the grant AICO/2021/302 (Generalitat Valenciana). The author CP was partially supported by CMUP (UID/-MAT/00144/2013), which is funded by Fundacao para a Ciencia e Tecnologia (FCT) (Portugal) with national (MEC) and European structural funds European Regional Development Fund (FEDER), under the partnership agreement PT2020. es_ES
dc.language Inglés es_ES
dc.publisher Springer es_ES
dc.relation.ispartof European Physical Journal Plus es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Probabilistic analysis of a foundational class of generalized second-order linear differential equations in Classic Mechanics es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1140/epjp/s13360-022-02691-x es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-115270GB-I00/ES/ECUACIONES DIFERENCIALES ALEATORIAS. CUANTIFICACION DE LA INCERTIDUMBRE Y APLICACIONES/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//AICO%2F2021%2F302/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UID%2FMAT%2F00144%2F2013/PT es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Instituto Universitario de Matemática Multidisciplinar - Institut Universitari de Matemàtica Multidisciplinària es_ES
dc.contributor.affiliation Universitat Politècnica de València. Facultad de Administración y Dirección de Empresas - Facultat d'Administració i Direcció d'Empreses es_ES
dc.description.bibliographicCitation Burgos-Simon, C.; Cortés, J.; López-Navarro, E.; Pinto, CMA.; Villanueva Micó, RJ. (2022). Probabilistic analysis of a foundational class of generalized second-order linear differential equations in Classic Mechanics. European Physical Journal Plus. 137(5):1-12. https://doi.org/10.1140/epjp/s13360-022-02691-x es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1140/epjp/s13360-022-02691-x 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 137 es_ES
dc.description.issue 5 es_ES
dc.identifier.eissn 2190-5444 es_ES
dc.relation.pasarela S\460288 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder AGENCIA ESTATAL DE INVESTIGACION es_ES
dc.contributor.funder European Regional Development Fund es_ES
dc.contributor.funder Fundação para a Ciência e a Tecnologia, Portugal es_ES
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