Numerical solution of the Burgers equation with Neumann boundary noise

In this paper we investigate the numerical solution of the one-dimensional Burgers equation with Neumann boundary noise. For the discretization scheme we use the Galerkin approximation in space and the exponential Euler method in time. The impact of the boundary noise on the solution is discussed in several numerical examples. Moreover, we analyze and illustrate some properties of the stochastic term and study the convergence numerically.