In [B. Gustafsson and E. Mossberg, SIAM J. Sci. Comput., 26 (2004), pp. 259--271], a fourth order one-step method was constructed for the solution of wave propagation problems. The method is based on the first order system form of the PDE and uses a staggered grid both in space and time. The method was also applied with good results to a problem with discontinuous coefficients without using any special procedure across the discontinuity. In this paper we will analyze a model problem from acoustics and demonstrate the theoretical foundation for this behavior. Furthermore, we shall present more detailed numerical experiments which confirm the theoretical results.
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Gustafsson et al. (2004) studied this question.
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