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Improving adaptive generalized polynomial chaos method to solve nonlinear random differential equations by the random variable transformation technique

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Improving adaptive generalized polynomial chaos method to solve nonlinear random differential equations by the random variable transformation technique

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dc.contributor.author Cortés, J.-C. es_ES
dc.contributor.author Romero, José-Vicente es_ES
dc.contributor.author Roselló, María-Dolores es_ES
dc.contributor.author Villanueva Micó, Rafael Jacinto es_ES
dc.date.accessioned 2018-07-09T06:43:41Z
dc.date.available 2018-07-09T06:43:41Z
dc.date.issued 2017 es_ES
dc.identifier.issn 1007-5704 es_ES
dc.identifier.uri http://hdl.handle.net/10251/105538
dc.description.abstract [EN] Generalized polynomial chaos (gPC) is a spectral technique in random space to represent random variables and stochastic processes in terms of orthogonal polynomials of the Askey scheme. One of its most fruitful applications consists of solving random differential equations. With gPC, stochastic solutions are expressed as orthogonal polynomials of the input random parameters. Different types of orthogonal polynomials can be chosen to achieve better convergence. This choice is dictated by the key correspondence between the weight function associated to orthogonal polynomials in the Askey scheme and the probability density functions of standard random variables. Otherwise, adaptive gPC constitutes a complementary spectral method to deal with arbitrary random variables in random differential equations. In its original formulation, adaptive gPC requires that both the unknowns and input random parameters enter polynomially in random differential equations. Regarding the inputs, if they appear as non-polynomial mappings of themselves, polynomial approximations are required and, as a consequence, loss of accuracy will be carried out in computations. In this paper an extended version of adaptive gPC is developed to circumvent these limitations of adaptive gPC by taking advantage of the random variable transformation method. A number of illustrative examples show the superiority of the extended adaptive gPC for solving nonlinear random differential equations. In addition, for the sake of completeness, in all examples randomness is tackled by nonlinear expressions. es_ES
dc.description.sponsorship This work has been partially supported by the Ministerio de Economia y Competitividad grants MTM2013-41765-P.
dc.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation MINISTERIO DE ECONOMIA INDUSTRIA Y COMPETITIVIDAD /MTM2013-41765-P es_ES
dc.relation.ispartof Communications in Nonlinear Science and Numerical Simulation es_ES
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Uncertainty es_ES
dc.subject Nonlinear random differential equations es_ES
dc.subject Adaptive generalized polynomial chaos es_ES
dc.subject Random variable transformation technique es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Improving adaptive generalized polynomial chaos method to solve nonlinear random differential equations by the random variable transformation technique es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1016/j.cnsns.2017.02.011 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 Cortés, J.; Romero, J.; Roselló, M.; Villanueva Micó, RJ. (2017). Improving adaptive generalized polynomial chaos method to solve nonlinear random differential equations by the random variable transformation technique. Communications in Nonlinear Science and Numerical Simulation. 50:1-15. doi:10.1016/j.cnsns.2017.02.011 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://doi.org/10.1016/j.cnsns.2017.02.011 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 15 es_ES
dc.type.version info:eu repo/semantics/publishedVersion es_ES
dc.description.volume 50 es_ES
dc.relation.pasarela 327148 es_ES
dc.contributor.funder MINISTERIO DE ECONOMIA INDUSTRIA Y COMPETITIVIDAD es_ES


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