NDLI: A homotopic Galerkin approach to the solution of the Fokker-Planck-Kolmogorov equation

Content Provider	IEEE Xplore Digital Library
Author	Chakravorty, S.
Copyright Year	2006
Description	Author affiliation: Fac. of Aerosp. Eng., Texas A&M Univ., College Station, TX (Chakravorty, S.)
Abstract	In this paper, we present a homotopic Galerkin approach to the solution of the Fokker-Planck-Kolmogorov equation. We argue that the ideal Hilbert space to approximate the exact solution, psi* is the space $L_{2}(dPsi)$ where dPsi is the probability measure induced on $R_{n}$ by the solution psi* itself. We show that given an initial approximation of the exact solution which is sufficiently close to the exact solution, we can obtain the exact solution iteratively by propagating the solution over sufficiently small time intervals using the Galerkin projection method. Further, we show that given a family of dynamical systems, $D_{P},$ indexed by the homotopy parameter p isin [0,1], where the dynamical system corresponding to p = 0 is a system whose associated Fokker-Planck equation can be solved and p = 1 is the dynamical system of interest, and such that the associated solutions to the corresponding Fokker-Planck equations can be changed smoothly by slowly varying the homotopy parameter, the exact solution can be obtained recursively, using the Galerkin projection method, starting with the solution to the Fokker-Planck equation associated with the dynamical system $D_{0}$
Sponsorship	American Automatic Control Council IFAC
File Size	220817
File Format	PDF
ISBN	1424402093
e-ISBN	1424402107
DOI	10.1109/ACC.2006.1656449
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-06-14
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	American Automatic Control Council(AACC)
Subject Keyword	Integral equations Moment methods Differential equations Partial differential equations Hilbert space Stochastic systems Indium tin oxide Probability density function Aerospace engineering Iterative methods
Content Type	Text
Resource Type	Article

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