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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 norm. The theoretical result is verified by a numerical experiment.

A New Numerical Approximation Method for Two-Dimensional Wave Equation with Neumann Damped Boundary