Toward a solution of a class of non-linear stochastic perturbed PDEs using automated WHEP algorithm

DOI10.1016/j.apm.2013.01.038zbMath1426.60093OpenAlexW2016022344MaRDI QIDQ1789014

Mohamed A. El-Beltagy, Magdy A. El-Tawil

Publication date: 9 October 2018

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2013.01.038

zbMATH Keywords

stochastic differential equationnonlinear differential equationsperturbation methodWiener-Hermite expansionautomated algorithmswhep

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Isotropic turbulence; homogeneous turbulence (76F05)

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Statistical measures approximations for the Gaussian part of the stochastic nonlinear damped Duffing oscillator solution process under the application of Wiener Hermite expansion linked by the multi-step differential transformed method ⋮ Computing probabilistic solutions of the Bernoulli random differential equation ⋮ Development of a fractional Wiener-Hermite expansion for analyzing the fractional stochastic models ⋮ A numerical modeling and its computational implementing simulation for generating distributions of the complicated random variable transformations with applications ⋮ A mean square chain rule and its application in solving the random Chebyshev differential equation ⋮ A mixed spectral treatment for the stochastic models with random parameters ⋮ Solution of the stochastic heat equation with nonlinear losses using Wiener-Hermite expansion

Cites Work

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• General stochastic oscillatory systems
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• Application of Wiener-Hermite Expansion to Nonstationary Random Vibration of a Duffing Oscillator
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• Solution of Stochastic Cubic and Quintic Nonlinear Diffusion Equation Using WHEP, Pickard and HPM Methods
• Use of the Wiener—Hermite expansion for nearly normal turbulence
• Relationship between a Wiener–Hermite expansion and an energy cascade
• Application of the Wiener-Hermite Expansion to the Diffusion of a Passive Scalar in a Homogeneous Turbulent Flow

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