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Constructing reliable approximations of the probability density function to the random heat PDE via a finite difference scheme

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Constructing reliable approximations of the probability density function to the random heat PDE via a finite difference scheme

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dc.contributor.author Calatayud, J. es_ES
dc.contributor.author Cortés, J.-C. es_ES
dc.contributor.author Díaz, J.A. es_ES
dc.contributor.author Jornet, M. es_ES
dc.date.accessioned 2021-02-10T04:31:28Z
dc.date.available 2021-02-10T04:31:28Z
dc.date.issued 2020-05 es_ES
dc.identifier.issn 0168-9274 es_ES
dc.identifier.uri http://hdl.handle.net/10251/160979
dc.description.abstract [EN] We study the random heat partial differential equation on a bounded domain assuming that the diffusion coefficient and the boundary conditions are random variables, and the initial condition is a stochastic process. Under general conditions, this stochastic system possesses a unique solution stochastic process in the almost sure and mean square senses. To quantify the uncertainty for this solution process, the computation of the probability density function is a major goal. By using a random finite difference scheme, we approximate the stochastic solution at each point by a sequence of random variables, whose probability density functions are computable, i.e., we construct a sequence of approximating density functions. We include numerical experiments to illustrate the applicability of our method. es_ES
dc.description.sponsorship This work has been supported by the Spanish Ministerio de Economia y Competitividad grant MTM2017-89664-P. The co-author Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo (PAID), Universitat Politecnica de Valencia. es_ES
dc.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation.ispartof Applied Numerical Mathematics es_ES
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Uncertainty quantification es_ES
dc.subject Random heat partial differential equation es_ES
dc.subject Finite difference scheme es_ES
dc.subject Probability density function es_ES
dc.subject Numerical method es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Constructing reliable approximations of the probability density function to the random heat PDE via a finite difference scheme es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1016/j.apnum.2020.01.012 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, J.; Cortés, J.; Díaz, J.; Jornet, M. (2020). Constructing reliable approximations of the probability density function to the random heat PDE via a finite difference scheme. Applied Numerical Mathematics. 151:413-424. https://doi.org/10.1016/j.apnum.2020.01.012 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1016/j.apnum.2020.01.012 es_ES
dc.description.upvformatpinicio 413 es_ES
dc.description.upvformatpfin 424 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 151 es_ES
dc.relation.pasarela S\400592 es_ES
dc.contributor.funder Agencia Estatal de Investigación es_ES
dc.contributor.funder Universitat Politècnica de València es_ES
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