Abstract
The lattice Boltzmann method has been applied to calculate the probability density function of a nonlinear system subjected to white noise excitation, because of its advantage that the algorithm of the lattice Boltzmann method easily satisfies the both conditions that probability is non-negative and total probability equal to one. The probability density function is governed by partial differential equation known as the Fokker-Planck equation. The local rule of the lattice Boltzmann method is obtained by assuming Fokker-Planck equation as a kind of diffusion-drift partial differential equation. The probability densities of a Duffing and a Van del Pol oscillator are calculated and compared with exact solution or Monte Carlo simulation results.
