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

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    Type
    Presentation
    Authors
    El Beltagy, Mohamed
    Date
    2016-01-06
    Permanent link to this record
    http://hdl.handle.net/10754/624853
    
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    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)
    Additional Links
    http://mediasite.kaust.edu.sa/Mediasite/Play/8d6fb45c664943fcbfe8410d44c2e9491d?catalog=ca65101c-a4eb-4057-9444-45f799bd9c52
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    Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)

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