Numerical Solution of Stochastic Nonlinear Fractional Differential Equations

Handle URI:
http://hdl.handle.net/10754/624054
Title:
Numerical Solution of Stochastic Nonlinear Fractional Differential Equations
Authors:
El-Beltagy, Mohamed A.; Al-Juhani, Amnah
Abstract:
Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.
Conference/Event name:
Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)
Issue Date:
7-Jan-2015
Type:
Poster
Appears in Collections:
Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)

Full metadata record

DC FieldValue Language
dc.contributor.authorEl-Beltagy, Mohamed A.en
dc.contributor.authorAl-Juhani, Amnahen
dc.date.accessioned2017-06-05T08:35:46Z-
dc.date.available2017-06-05T08:35:46Z-
dc.date.issued2015-01-07-
dc.identifier.urihttp://hdl.handle.net/10754/624054-
dc.description.abstractUsing Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.en
dc.titleNumerical Solution of Stochastic Nonlinear Fractional Differential Equationsen
dc.typePosteren
dc.conference.dateJanuary 6-9, 2015en
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)en
dc.conference.locationKAUSTen
dc.contributor.institutionEffat Universityen
dc.contributor.institutionNorthern Borders University, Araren
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.