Computational uncertainty quantification for random non-autonomous second order linear differential equations via adapted gPC: a comparative case study with random Fröbenius method and Monte Carlo simulation
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INVESTIGACIONMetadatos
Título
Computational uncertainty quantification for random non-autonomous second order linear differential equations via adapted gPC: a comparative case study with random Fröbenius method and Monte Carlo simulationFecha de publicación
2018-12Editor
De GruyterISSN
2391-5455Cita bibliográfica
Calatayud, J., Cortés, J. C., & Jornet, M. (2018). Computational uncertainty quantification for random non-autonomous second order linear differential equations via adapted gPC: a comparative case study with random Fröbenius method and Monte Carlo simulation. Open Mathematics, 16(1), 1651-1666.Tipo de documento
info:eu-repo/semantics/articleVersión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
This paper presents a methodology to quantify computationally the uncertainty in a class of differential equations often met in Mathematical Physics, namely random non-autonomous second-order linear differential ... [+]
This paper presents a methodology to quantify computationally the uncertainty in a class of differential equations often met in Mathematical Physics, namely random non-autonomous second-order linear differential equations, via adaptive generalized Polynomial Chaos (gPC) and the stochastic Galerkin projection technique. Unlike the random Fröbenius method, which can only deal with particular random linear differential equations and needs the random inputs (coefficients and forcing term) to be analytic, adaptive gPC allows approximating the expectation and covariance of the solution stochastic process to general random second-order linear differential equations. The random inputs are allowed to functionally depend on random variables that may be independent or dependent, both absolutely continuous or discrete with infinitely many point masses. These hypotheses include a wide variety of particular differential equations, which might not be solvable via the random Fröbenius method, in which the random input coefficients may be expressed via a Karhunen-Loève expansion. [-]
Publicado en
Open Mathematics, Vol.16, Issue 1 (2018)Entidad financiadora
Ministerio de Economía y Competitividad | Universitat Politècnica de València
Código del proyecto o subvención
MTM2017–89664–P
Título del proyecto o subvención
Programa de Ayudas de Investigación y Desarrollo (PAID)
Derechos de acceso
© 2018 Calatayud et al., published by De Gruyter
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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