Search results for "Weighted residuals method"

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Approximate solution of the Fokker-Planck-Kolmogorov equation

2002

The aim of this paper is to present a thorough investigation of approximate techniques for estimating the stationary and non-stationary probability density function (PDF) of the response of nonlinear systems subjected to (additive and/or multiplicative) Gaussian white noise excitations. Attention is focused on the general scheme of weighted residuals for the approximate solution of the Fokker-Planck-Kolmogorov (FPK) equation. It is shown that the main drawbacks of closure schemes, such as negative values of the PDF in some regions, may be overcome by rewriting the FPK equation in terms of log-probability density function (log-PDF). The criteria for selecting the set of weighting functions i…

Mechanical EngineeringMultiplicative functionAerospace EngineeringOcean EngineeringStatistical and Nonlinear PhysicsProbability density functionWhite noiseCondensed Matter PhysicsMultiplicative noiseWeightingNonlinear systemsymbols.namesakeNuclear Energy and EngineeringGaussian noiseProbability density functionsymbolsApplied mathematicsFokker–Planck equationWeighted residuals methodSafety Risk Reliability and QualityCivil and Structural EngineeringMathematical physicsMathematicsFokker-Planck-Kolmogorov equation
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