Numerical Solution of the Fokker‐Planck Equation with Time‐Discontinuous Galerkin Methods

Abstract

The response of non-linear dynamic systems under white noise excitation possesses Markov characteristics. The evolution of the probability density of the system response is represented by the Fokker-Planck equation, which characterizes advection and diffusion. The solution probability density distribution often possesses high gradients. Therefore an efficient numerical solution technique based on a discontinuous Galerkin approximation in the time domain is proposed for the solution of the Fokker-Planck equation.