A NUMERICAL METHOD FOR PROPAGATION OF UNCERTAINTY IN NONLINEAR SYSTEMS

Abstract

A numerical method is presented which propagates uncertainty through dynamical systems. It is a fast method of solving the Fokker-Planck equation in the special case of zero diffusion, and requires only that sufficient moments of the initial joint density function be known to adequately characterize it. The method relies upon approximating a continuous density function with a discrete density function. For some systems an interesting linearity condition holds for the uncertainty.

INDEX TERMS:

• Nonlinear system
• Fokker-Pianck equation
• uncertainty propagation
• numerical methods
• chaos
• chaotic systems