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The approximate solutions of FPK equations in high dimensions for some nonlinear stochastic dynamic systems
Guo-Kang Er; Vai Pan Iu
2011-11-01
Source PublicationCommunications in Computational Physics
ISSN1815-2406
Volume10Issue:5Pages:1241-1256
Abstract

The probabilistic solutions of the nonlinear stochastic dynamic (NSD) systems with polynomial type of nonlinearity are investigated with the subspace-EPC method. The space of the state variables of large-scale nonlinear stochastic dynamic system excited by white noises is separated into two subspaces. Both sides of the Fokker-Planck-Kolmogorov (FPK) equation corresponding to the NSD system is then integrated over one of the subspaces. The FPK equation for the joint probability density function of the state variables in another subspace is formulated. Therefore, the FPK equation in low dimensions is obtained from the original FPK equation in high dimensions and it makes the problem of obtaining the probabilistic solutions of largescale NSD systems solvable with the exponential polynomial closure method. Examples about the NSD systems with polynomial type of nonlinearity are given to show the effectiveness of the subspace-EPC method in these cases. 

KeywordFokker-planck-kolmogorov Equation Large-scale Systems Nonlinear Stochastic Dynamic Systems Probability Density Function Subspace
DOIhttps://doi.org/10.4208/cicp.140710.210111a
URLView the original
Indexed BySCI
Language英语
WOS Research AreaPhysics
WOS SubjectPhysics, Mathematical
WOS IDWOS:000298764200007
PublisherGLOBAL SCIENCE PRESS, ROOM 3208, CENTRAL PLAZA, 18 HARBOUR RD, WANCHAI, HONG KONG 00000, PEOPLES R CHINA
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING
AffiliationFaculty of Science and Technology, University of Macau, Macau SAR, P. R. China
First Author AffilicationFaculty of Science and Technology
Recommended Citation
GB/T 7714
Guo-Kang Er,Vai Pan Iu. The approximate solutions of FPK equations in high dimensions for some nonlinear stochastic dynamic systems[J]. Communications in Computational Physics,2011,10(5):1241-1256.
APA Guo-Kang Er,&Vai Pan Iu.(2011).The approximate solutions of FPK equations in high dimensions for some nonlinear stochastic dynamic systems.Communications in Computational Physics,10(5),1241-1256.
MLA Guo-Kang Er,et al."The approximate solutions of FPK equations in high dimensions for some nonlinear stochastic dynamic systems".Communications in Computational Physics 10.5(2011):1241-1256.
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