Approximate stationary density of the nonlinear dynamical systems excited with white noise

In this paper, obtaining an approximate solution of the Fokker-Planck-Kolmogorov (FPK) equation using compactly supported functions has been discussed. With specific choice of such functions as piecewise multivariable polynomials which are supported on ellipsoidal regions, the parameters to be determined can be considerably decreased compared to the multi-Gaussian closure scheme. An example commonly considered in the literature has been analyzed and the proposed method has been compared with the multi-Gaussian closure scheme. The simulation results indicate that the new scheme is quite successful even if the driving noise is not white Gaussian, but has an exponential correlation function with small correlation time.