Approximate analysis of nonlinear stochastic differential equations using certain generalized quasi-moment functions
type: Item
instance of: scholarly article
title: Approximate analysis of nonlinear stochastic differential equations using certain generalized quasi-moment functions
zbMATH Open document ID: 0586.73200
DOI: 10.1007/BF01181663
author: L. Sperling
published in: Acta Mechanica
publication date: 1986-01-01T00:00:00Z
review text: The application and the advantages of the method of certain generalized quasi-moment functions are demonstrated by way of a simple mechanical example. The stress of the considered viscoelastic beam, subjected to a stochastically variable temperature, is described by a nonlinear (case a) or a linear (case b) equation of first order with stochastic coefficients resulting by passing Gaussian white noise through a linear shaping filter. As a result, the final differential equation system is nonlinear also in case b. The mean value, the variance (for the cases a and b), the covariance function and the spectral density (for case b only) of the stress are estimated by means of linear quasi-moment equations with good convergence. In contrast to this, the results which were obtained by the normal distribution method, here being used as the basic approximation, are affected with great deviations.
Mathematics Subject Classification ID: 74A15
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 74K10
zbMATH DE Number: 3940990
zbMATH Keywords: nonlinear equation of first order
zbMATH Keywords: linear equation
zbMATH Keywords: Pugachev equation
zbMATH Keywords: generalized quasi-moment functions
zbMATH Keywords: viscoelastic beam
zbMATH Keywords: stochastically variable temperature
zbMATH Keywords: stochastic coefficients
zbMATH Keywords: Gaussian white noise
zbMATH Keywords: linear shaping filter
zbMATH Keywords: mean value
zbMATH Keywords: variance
zbMATH Keywords: covariance function
zbMATH Keywords: spectral density
zbMATH Keywords: estimated
zbMATH Keywords: linear quasi-moment equations
zbMATH Keywords: convergence
MaRDI profile type: Publication
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cites work: A study of some systems in the neighbourhood of S4.4
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full work available at URL: https://doi.org/10.1007/bf01181663
OpenAlex ID: W1996981342
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description: scientific article; zbMATH DE number 3940990