Solution of stochastic nonlinear PDEs using Wiener-Hermite expansion of high orders

Handle URI:
http://hdl.handle.net/10754/624853
Title:
Solution of stochastic nonlinear PDEs using Wiener-Hermite expansion of high orders
Authors:
El Beltagy, Mohamed
Abstract:
In this work, the Wiener-Hermite Expansion (WHE) is used to solve stochastic nonlinear PDEs excited with noise. The generation of the equivalent set of deterministic integro-differential equations is automated and hence allows for high order terms of WHE. The automation difficulties are discussed, solved and implemented to output the final system to be solved. A numerical Pikard-like algorithm is suggested to solve the resulting deterministic system. The automated WHE is applied to the 1D diffusion equation and to the heat equation. The results are compared with previous solutions obtained with WHEP (WHE with perturbation) technique. The solution obtained using the suggested WHE technique is shown to be the limit of the WHEP solutions with infinite number of corrections. The automation is extended easily to account for white-noise of higher dimension and for general nonlinear PDEs.
Conference/Event name:
Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)
Issue Date:
6-Jan-2016
Type:
Presentation
Additional Links:
http://mediasite.kaust.edu.sa/Mediasite/Play/8d6fb45c664943fcbfe8410d44c2e9491d?catalog=ca65101c-a4eb-4057-9444-45f799bd9c52
Appears in Collections:
Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)

Full metadata record

DC FieldValue Language
dc.contributor.authorEl Beltagy, Mohameden
dc.date.accessioned2017-06-08T06:32:29Z-
dc.date.available2017-06-08T06:32:29Z-
dc.date.issued2016-01-06-
dc.identifier.urihttp://hdl.handle.net/10754/624853-
dc.description.abstractIn this work, the Wiener-Hermite Expansion (WHE) is used to solve stochastic nonlinear PDEs excited with noise. The generation of the equivalent set of deterministic integro-differential equations is automated and hence allows for high order terms of WHE. The automation difficulties are discussed, solved and implemented to output the final system to be solved. A numerical Pikard-like algorithm is suggested to solve the resulting deterministic system. The automated WHE is applied to the 1D diffusion equation and to the heat equation. The results are compared with previous solutions obtained with WHEP (WHE with perturbation) technique. The solution obtained using the suggested WHE technique is shown to be the limit of the WHEP solutions with infinite number of corrections. The automation is extended easily to account for white-noise of higher dimension and for general nonlinear PDEs.en
dc.relation.urlhttp://mediasite.kaust.edu.sa/Mediasite/Play/8d6fb45c664943fcbfe8410d44c2e9491d?catalog=ca65101c-a4eb-4057-9444-45f799bd9c52en
dc.titleSolution of stochastic nonlinear PDEs using Wiener-Hermite expansion of high ordersen
dc.typePresentationen
dc.conference.dateJanuary 5-10, 2016en
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)en
dc.conference.locationKAUSTen
dc.contributor.institutionEffat Universityen
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