Investigations on the numerical solution of the Fokker‐Planck equation with discontinuous Galerkin Methods

Abstract

Nonlinear dynamic systems under stochastic excitation possess Markov characteristics. Thus, their stochastic equation of motion can be transformed into the Fokker‐Planck equation which describes the evolution of the probability density. A discontinuous Galerkin (DG) method is applied to solve the Fokker‐Planck equation. This method provides numerical stability as well as accuracy and is able to treat discontinuities of the solution. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)