Strong Convergence of a Verlet Integrator for the Semilinear Stochastic Wave Equation

The full discretization of the semilinear stochastic wave equation is considered. discontinuous Galerkin finite element method used in space and analyzed a semigroup framework, an explicit position Verlet scheme for temporal approximation. We study stability under CFL condition prove optimal strong convergence rates fully discrete scheme. Numerical experiments illustrate our theoretical results. Further, we analyze bound expected energy numerically show excellent agreement with exact solution.