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Methodology for the solutions of some reduced Fokker-Planck equations in high dimensions
Er G.K.
2011
Source PublicationAnnalen der Physik (Leipzig)
ISSN33804
Volume523Issue:3Pages:247
AbstractIn this paper, a new methodology is formulated for solving the reduced Fokker-Planck (FP) equations in high dimensions based on the idea that the state space of large-scale nonlinear stochastic dynamic system is split into two subspaces. The FP equation relevant to the nonlinear stochastic dynamic system is then integrated over one of the subspaces. The FP equation for the joint probability density function of the state variables in another subspace is formulated with some techniques. Therefore, the FP equation in high-dimensional state space is reduced to some FP equations in low-dimensional state spaces, which are solvable with exponential polynomial closure method. Numerical results are presented and compared with the results from Monte Carlo simulation and those from equivalent linearization to show the effectiveness of the presented solution procedure. It attempts to provide an analytical tool for the probabilistic solutions of the nonlinear stochastic dynamics systems arising from statistical mechanics and other areas of science and engineering. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
KeywordFokker-Planck equation large-scale systems Nonlinear stochastic dynamics state space split.
DOI10.1002/andp.201010465
URLView the original
Language英语
The Source to ArticleScopus
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Cited Times [WOS]:36   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING
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Er G.K.. Methodology for the solutions of some reduced Fokker-Planck equations in high dimensions[J]. Annalen der Physik (Leipzig),2011,523(3):247.
APA Er G.K..(2011).Methodology for the solutions of some reduced Fokker-Planck equations in high dimensions.Annalen der Physik (Leipzig),523(3),247.
MLA Er G.K.."Methodology for the solutions of some reduced Fokker-Planck equations in high dimensions".Annalen der Physik (Leipzig) 523.3(2011):247.
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