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Zbl 1077.65092
Gustafsson, Bertil; Wahlund, Per
Time compact difference methods for wave propagation in discontinuous media. (English)
[J] SIAM J. Sci. Comput. 26, No. 1, 272-293 (2004). ISSN 1064-8275; ISSN 1095-7197/e

Summary: {\it B. Gustafsson} and {\it 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 2000:: *65M06 Finite difference methods (IVP of PDE)
35L05 Wave equation
76Q05 Density waves (fluid mechanics)
76M20 Finite difference methods

Keywords: finite difference methods; high order methods; wave equation; discontinuous media; numerical experiments

Citations: Zbl 1075.65112

Cited in: Zbl 1136.65084

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