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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Title
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 simulationDate
2018-12Publisher
De GruyterISSN
2391-5455Bibliographic citation
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.Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/publishedVersionSubject
Abstract
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. [-]
Is part of
Open Mathematics, Vol.16, Issue 1 (2018)Funder Name
Ministerio de Economía y Competitividad | Universitat Politècnica de València
Project code
MTM2017–89664–P
Project title or grant
Programa de Ayudas de Investigación y Desarrollo (PAID)
Rights
© 2018 Calatayud et al., published by De Gruyter
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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