Methodological Approaches for the Fokker-Planck Equation Associated to Nonlinear Stochastic Differential Systems with Uncertain Parameters

摘要

This paper is an extension of work originally presented at the World Conference on Complex Systems. In this paper, methodological approaches and numerical procedures are elaborated for nonlinear stochastic differential equations with uncertain parameters. The associated Fokker-Planck equation is used to get the distribution function. Mathematical developments based on the meshfree method with radial basis functions and on exponential closure combined with Monte Carlo and conditional expectation methods are elaborated for numerical solutions. The obtained approximate solutions compare well with available solutions and the effectiveness and accuracy of the proposed methods are demonstrated.