Difference methods for time discretization of spectral fractional stochastic wave equation

Abstract

The time discretization of stochastic fractional wave equation is studied by using difference methods. Firstly, we use the rectangular formula to obtain a low-order time discretization, and its strong convergence order is less than 1 in the sense of mean squared L2-norm. Meanwhile, by modifying the low order method with trapezoidal rule, the convergence rate is improved at expenses of requiring some extra temporal regularity to the solution. The modified scheme has superlinear convergence rate under the mean squared L2-norm. Several numerical experiments are provided to confirm the theoretical error estimates.