Abstract
A two-level compact alternating direction implicit (ADI) method is constructed for solving second-order wave equations with periodic boundary conditions. By using an H 2 discrete energy method, it is shown that the compact ADI method is unconditionally convergent in the maximum norm with the convergence order of 2 in time and 4 in space. Asymptotic expansion, only in even powers of the mesh parameters (time step and spacings), of the difference solution is achieved. Using the expansion of the solution, high-order approximations could be achieved by Richardson extrapolations. Numerical experiments are included to support the theoretical results and show the effectiveness of our method.
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