Abstract
We consider an initial-boundary value problem for the n-dimensional wave equation, n⩾2, with the variable sound speed with the nonhomogeneous Dirichlet boundary conditions. We construct and study three-level in time and compact in space three-point in each spatial direction alternating direction implicit (ADI) schemes having the approximation orders O(ht2+|h|4) and O(ht4+|h|4) on the uniform rectangular mesh. The study includes stability bounds in the strong and weak energy norms, the discrete energy conservation law and the error bound of the order O(ht2+|h|4) for the first scheme as well as a short justification of the approximation order O(ht4+|h|4) for the second scheme. We also present results of numerical experiments.
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