On the Calculation of Stationary Solutions of Multi-Dimensional Fokker–Planck Equations by Orthogonal Functions
In this paper, nonlinear stochastic systems are investigatedvia associated Fokker–Planck equations. Their stationary solutions arecalculated by expansions into orthogonal functions, e.g. especiallyadjusted polynomials and Fourier series. The weighting functions of thenew polynomials are obtained by...
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| Veröffentlicht in: | Nonlinear dynamics 2000-03, Vol.21 (3), p.289-306 |
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| creator | Utz von Wagner Wedig, Walter V |
| description | In this paper, nonlinear stochastic systems are investigatedvia associated Fokker–Planck equations. Their stationary solutions arecalculated by expansions into orthogonal functions, e.g. especiallyadjusted polynomials and Fourier series. The weighting functions of thenew polynomials are obtained by the application of the stochasticaveraging method. The proposed analysis is demonstrated with severalexamples. The first one is a two-dimensional problem of nonlinearoscillators driven by white noise. The second one describes two-massoscillators with independent coloured noise excitations leading tosix-dimensional probability density functions. The next example ispresenting a system driven by both harmonic and stochastic excitationleading to three-dimensional probability density functions. Finally,oscillators with dry friction characteristics are examined. |
| doi_str_mv | 10.1023/A:1008389909132 |
| format | Article |
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| subjects | Dry friction Fourier series Mathematical analysis Nonlinear systems Orthogonal functions Oscillators Polynomials Probability density functions Probability theory Stochastic systems Weighting functions White noise |
| title | On the Calculation of Stationary Solutions of Multi-Dimensional Fokker–Planck Equations by Orthogonal Functions |
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