Generalized Wiener expansions for the numerical solution of random ordinary differential equations

In this work we discussed stochastic Galerkin Runge-Kutta methods for the numerical approximation of the solution of RODEs. Thereby we observed an unexpected reduction of the convergence order for an increasing polynomial degree of the truncated generalized Wiener expansion. To explain this behavior, we split up the error between the numerical approximation and the exact solution into two parts. The first one coming from the restriction to the finite-dimensional approximation space S and the second one coming from the time discretization of the underlying RKM.