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Time compact difference methods for wave propagation in discontinuous media. (English) Zbl 1077.65092

Summary: B. Gustafsson and E. Mossberg [SIAM J. Sci. Comput. 26, No. 1, 259–271 (2004; Zbl 1075.65112)] constructed a fourth order one-step method for the solution of wave propagation problems. The method is based on the first order system form of the partial differential equation 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.

We analyze a model problem from acoustics and demonstrate the theoretical foundation for this behavior. Furthermore, we present more detailed numerical experiments which confirm the theoretical results.


MSC:
65M06Finite difference methods (IVP of PDE)
35L05Wave equation (hyperbolic PDE)
76Q05Hydro- and aero-acoustics
76M20Finite difference methods (fluid mechanics)