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A second-order energy-preserving scheme is studied for the solution of the semilinear Cauchy Problem un uxx -uyy + u =0 (t > 0 ; x, y e R). Smooth data functions of compact support are prescribed at t = 0. On any time interval [0, 7"], second-order convergence (up to logarithmic corrections) to the exact solution is established in both the energy and uniform norms.

Convergence of a second-order scheme for semilinear hyperbolic equations in 2+1 dimensions