Gustafsson, Bertil; Wahlund, Per Time compact difference methods for wave propagation in discontinuous media. (English) Zbl 1077.65092 SIAM J. Sci. Comput. 26, No. 1, 272-293 (2004). 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. Cited in 1 ReviewCited in 24 Documents MSC: 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35L05 Wave equation 76Q05 Hydro- and aero-acoustics 76M20 Finite difference methods applied to problems in fluid mechanics Keywords:finite difference methods; high order methods; wave equation; discontinuous media; numerical experiments Citations:Zbl 1075.65112 PDFBibTeX XMLCite \textit{B. Gustafsson} and \textit{P. Wahlund}, SIAM J. Sci. Comput. 26, No. 1, 272--293 (2004; Zbl 1077.65092) Full Text: DOI