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An initial-boundary value problem for the $n$-dimensional wave equation isconsidered. A three-level explicit in time and conditionally stable 4th-ordercompact scheme constructed recently for $n=2$ and the square mesh isgeneralized to the case of any $n\geq 1$ and the rectangular uniform mesh.Another approach to approximate the solution at the first time level (notexploiting high-order derivatives of the initial functions) is suggested. Newstability bounds in the mesh energy norms and the discrete energy conservationlaws are given, and the 4th order error bound is rigorously proved.Generalizations to the cases of the non-uniform meshes in space and time aswell as of the wave equation with variable coefficients are suggested.

On properties of an explicit in time fourth-order vector compact scheme for the multidimensional wave equation