Piecewise optimal linearization method for nonlinear stochastic differential equations |
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Authors: | John O Eaves William P Reinhardt |
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Institution: | (1) Department of Chemistry-215, University of Colorado, 80309 Boulder, Colorado;(2) Joint Institute for Laboratory Astrophysics-440, University of Colorado, 80309 Boulder, Colorado;(3) National Bureau of Standards, 80309 Boulder, Colorado |
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Abstract: | A method for estimating the dynamical statistical properties of the solutions of nonlinear Langevin-type stochastic differential equations is presented. The non-linear equation is linearized within a small interval of the independent variable and statistical properties are expressed analytically within the interval. The linearization procedure is optimal in the sense of the Chebyshev inequality. Long-term behavior of the solution process is obtained by appropriately matching the approximate solutions at the boundaries between intervals. The method is applied to a model nonlinear equation for which the exact time-dependent moments can be obtained by numerical methods. The calculations demonstrate that the method represents a significant improvement over the method of statistical linearization in time regimes far from equilibrium.Supported in part by the National Science Foundation under Grants CHE77-16307 and PHY76-04761. |
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Keywords: | Nonlinear stochastic equations time-dependent moments statistical linearization piecewise optimal linearization |
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