Numerical approximation of higher-order solutions of the quadratic nonlinear stochastic oscillatory equation using WHEP technique
type: Item
instance of: scholarly article
title: Numerical approximation of higher-order solutions of the quadratic nonlinear stochastic oscillatory equation using WHEP technique
zbMATH Open document ID: 1397.34097
DOI: 10.1155/2013/685137
author: Mohamed A. El-Beltagy
author: Amnah S. Al-Johani
published in: Journal of Applied Mathematics
publication date: 2018-10-10T00:00:00Z
review text: Summary: This paper introduces higher-order solutions of the stochastic nonlinear differential equations with the Wiener-Hermite expansion and perturbation (WHEP) technique. The technique is used to study the quadratic nonlinear stochastic oscillatory equation with different orders, different number of corrections, and different strengths of the nonlinear term. The equivalent deterministic equations are derived up to third order and fourth correction. A model numerical integral solver is developed to solve the resulting set of equations. The numerical solver is tested and validated and then used in simulating the stochastic quadratic nonlinear oscillatory motion with different parameters. The solution ensemble average and variance are computed and compared in all cases. The current work extends the use of WHEP technique in solving stochastic nonlinear differential equations.
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 34A25
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 34C15
zbMATH DE Number: 6950820
Wikidata QID: Q59003793
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/685137
OpenAlex ID: W2052472510
DBLP publication ID: journals/jam/El-BeltagyA13
description: scientific article; zbMATH DE number 6950820