Approximate solution of the Fokker-Planck-Kolmogorov equation

Risultato della ricerca: Articlepeer review

92 Citazioni (Scopus)


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 in order to obtain improved estimates of the response PDF are discussed in detail. Finally, a simple and very effective iterative solution procedure is proposed. © 2002 Published by Elsevier Science Ltd.
Lingua originaleEnglish
pagine (da-a)369-384
Numero di pagine16
RivistaProbabilistic Engineering Mechanics
Stato di pubblicazionePublished - 2002

All Science Journal Classification (ASJC) codes

  • ???subjectarea.asjc.3100.3109???
  • ???subjectarea.asjc.2200.2205???
  • ???subjectarea.asjc.2100.2104???
  • ???subjectarea.asjc.3100.3104???
  • ???subjectarea.asjc.2200.2202???
  • ???subjectarea.asjc.2200.2212???
  • ???subjectarea.asjc.2200.2210???


Entra nei temi di ricerca di 'Approximate solution of the Fokker-Planck-Kolmogorov equation'. Insieme formano una fingerprint unica.

Cita questo