Abstract
In this paper, we propose a family of new three-level compact alternating direction implicit (ADI) difference schemes for solving a linear wave equation with a nonlinear damping function. By using a fourth-order accurate scheme to approximate the exact solution at the first time level, it is shown through the energy method that these difference schemes have fourth-order accuracy in space and second-order accuracy in time with respect to H1- and L∞-norms. A class of Richardson extrapolation algorithms based on three time-grid parameters are presented to obtain approximate solution of fourth-order accuracy in both time and space in L∞-norm. Numerical experiments are performed to support our theoretical results and test the accuracy and efficiency of our algorithms.
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