Numerical simulation of nonlinear stochastic differential system with uncertain parameters

In this work the Fokker-Planck-Kolmogorov equation associated to nonlinear stochastic differential equations with uncertain parameters is used to obtain the associated distribution functions. The exponential closure method is extended to the considered random systems with uncertain parameters. Methodological approaches and numerical procedures based on meshfree method with radial basis function (RBF) and exponential closure are elaborated for the considered random equations. The obtained approximate solutions are well compared with the exact solution and Monte Carlo based results. For physical application, the dynamic behavior of beams with uncertain parameters excited by uniformly distributed Gaussian white noise is considered. The accuracy, effectiveness and advantages of the developed procedures in analyzing the probabilistic solutions of nonlinear stochastic systems with uncertain parameters excited by Gaussian white noise are demonstrated.