On the convergence of adaptive gPC for non-linear random difference equations: Theoretical analysis and some practical recommendations
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http://dx.doi.org/10.22436/jnsa.011.09.06 |
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Title
On the convergence of adaptive gPC for non-linear random difference equations: Theoretical analysis and some practical recommendationsDate
2018-06-19Publisher
International Scientific Research PublicationsISSN
2008-1898; 2008-1901Bibliographic citation
Calatayud, J., Cortés, J. C., & Jornet, M. (2018). On the convergence of adaptive gPC for non-linear random difference equations: Theoretical analysis and some practical recommendations. Journal of Nonlinear Sciences & Applications (JNSA), 11(9).Type
info:eu-repo/semantics/articlePublisher version
https://www.isr-publications.com/jnsa/articles-7147-on-the-convergence-of-adapti ...Version
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Abstract
In this paper, the application of adaptive generalized polynomial chaos (gPC) to quantify the uncertainty for non-linear
random difference equations is analyzed. It is proved in detail that, under certain assumptions, ... [+]
In this paper, the application of adaptive generalized polynomial chaos (gPC) to quantify the uncertainty for non-linear
random difference equations is analyzed. It is proved in detail that, under certain assumptions, the stochastic Galerkin projection
technique converges algebraically in mean square to the solution process of the random recursive equation. The effect of the
numerical errors on the convergence is also studied. A full numerical experiment illustrates our theoretical findings and gives
useful insights to reduce the accumulation of numerical errors in practice. [-]
Is part of
Journal of Nonlinear Sciences and Applications (JNSA), Vol. 11 (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)
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