Response of stochastic dynamical systems driven by additive Gaussian and Poisson white noise: Solution of a forward generalized Kolmogorov equation by a spectral finite difference method

Steven F. Wojtkiewicz, Erik A. Johnson, Lawrence Bergman, Mircea Grigoriu, Billie F. Spencer

Research output: Contribution to journalArticle

Abstract

A numerical method is given for the solution of the probability density function of the response process of memoryless one- and two-state dynamical systems having polynomial restoring forces and which are subjected to a combination of Gaussian and Poisson white noises. The method employs the Fourier transformed forward generalized Kolmogorov equation to arrive at an initial-boundary value problem for the characteristic function, which is solved using a high-order finite difference procedure. The probability density function is recovered by numerical inverse Fourier transformation. Several examples are given, the results of which are compared with analytical solutions where available and with simulation otherwise.

Original languageEnglish (US)
Pages (from-to)73-89
Number of pages17
JournalComputer Methods in Applied Mechanics and Engineering
Volume168
Issue number1-4
DOIs
StatePublished - Jan 6 1999
Externally publishedYes

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

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