Weak approximation of the stochastic wave equation

We investigate the accuracy of approximation of E [ φ ( u ( t ) ) ] , where { u ( t ) : t ∈ [ 0 , ∞ ) } is the solution of the stochastic wave equation driven by the space–time white noise and φ is an R -valued function defined on the Hilbert space L 2 ( R ) . The approximation is done by the leap-frog scheme. We show that, under certain conditions on φ , the approximation by the leap-frog scheme is of order two.