Time compact difference methods for wave propagation in discontinuous media.

*(English)*Zbl 1077.65092Summary: *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:

65M06 | Finite difference methods (IVP of PDE) |

35L05 | Wave equation (hyperbolic PDE) |

76Q05 | Hydro- and aero-acoustics |

76M20 | Finite difference methods (fluid mechanics) |