A new numerical approximation method for two-dimensional wave equation with Neumann damped boundary (Q2196141)

Summary: In this paper, a fully discretized finite difference scheme is derived for two-dimensional wave equation with damped Neumann boundary condition. By discrete energy method, the proposed difference scheme is proven to be of second-order convergence and of unconditional stability with respect to both initial conditions and right-hand term in a proper discretized \(L^2\) norm. The theoretical result is verified by a numerical experiment.