Numerical Simulation of the Viscous Wave Equation with Stochastic Force

Abstract

We numerically investigate the dynamics of the solitary waves in the presence of external stochastic forces for the viscous wave equation. Since the analytic solutions of the considered problems are not expected available, finite volume element (FVE) method will be used in physical space and Monte Carlo (MC) sampling technique will be used in random space. Numerical results demonstrate that solitary wave profile is not strongly affected by the weak Gaussian white noise in our study. However, the noise with strong strength would destroy the propagation of solitary wave and increase the amplitude in some trajectories.