The semi‐analytical method for time‐dependent wave problems with uncertainties

This paper provides a constructive procedure for the computation of approximate solutions of random time‐dependent hyperbolic mean square partial differential problems. Based on the theoretical representation of the solution as an infinite random improper integral, obtained via the random Fourier transform method, a double approximation process is implemented. Firstly, a random Gauss‐Hermite quadrature is applied, and then, the evaluations at the nodes of the integrand are approximated by using a random Störmer numerical method. Numerical results are illustrated with examples.