Numerical solution of one-dimensional wave equation with stochastic parameters using generalized polynomial chaos expansion

This paper presents a numerical algorithm which is using generalized polynomial chaos combined with the finite difference method for the solution of the one-dimensional wave equation with stochastic physical parameters. The stochastic parameters are represented by the Hermite polynomial chaos. A spectral-finite difference model for the numerical solution is introduced using generalized polynomial chaos expansion. The general conditions for convergence and stability of numerical algorithms are derived. Finally, the method is applied to a vibrating string. Results are compared with those of a Monte Carlo simulation.