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 A. Bergman; Mircea Grigoriu; Billie F. Spencer

doi:10.1016/S0045-7825(98)00098-X

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 A. Bergman, Mircea Grigoriu, Billie F. Spencer

Aerospace Engineering

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	73-89
Number of pages	17
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	168
Issue number	1-4
DOIs	https://doi.org/10.1016/S0045-7825(98)00098-X
State	Published - Jan 6 1999

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
General Physics and Astronomy
Computer Science Applications

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10.1016/S0045-7825(98)00098-X

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Wojtkiewicz, S. F., Johnson, E. A., Bergman, L. A., Grigoriu, M., & Spencer, B. F. (1999). 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. Computer Methods in Applied Mechanics and Engineering, 168(1-4), 73-89. https://doi.org/10.1016/S0045-7825(98)00098-X

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. / Wojtkiewicz, Steven F.; Johnson, Erik A.; Bergman, Lawrence A. et al.
In: Computer Methods in Applied Mechanics and Engineering, Vol. 168, No. 1-4, 06.01.1999, p. 73-89.

Research output: Contribution to journal › Article › peer-review

Wojtkiewicz, SF, Johnson, EA, Bergman, LA, Grigoriu, M & Spencer, BF 1999, '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', Computer Methods in Applied Mechanics and Engineering, vol. 168, no. 1-4, pp. 73-89. https://doi.org/10.1016/S0045-7825(98)00098-X

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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

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