Abstract
In this paper, the method proposed recently by the author for the solution of probability density function (PDF) of nonlinear stochastic systems is presented in detail and extended for more general problems of stochastic differential equations (SDE), therefore the Fokker-Planck-Kolmogorov (FPK) equation is expressed in general form with no limitation on the degree of nonlinearity of the SDE, the type of δ-correlated excitations, the existence of multiplicative excitations, and the dimension of SDE or FPK equation. Examples are given and numerical results are provided for comparing with known exact solution to show the effectiveness of the method.
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The paper partially supported by the Foundation of the Research Committee of the University of Macao (No. 6851/96/UM, 628/97/UM)
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Er, G. Local galerkin method for the approximate solutions to general FPK equations. J. of Shanghai Univ. 3, 25–29 (1999). https://doi.org/10.1007/s11741-999-0024-5
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DOI: https://doi.org/10.1007/s11741-999-0024-5