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 |