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Time compact high order difference methods for wave propagation, 2D. (English) Zbl 1203.65136

Summary: In earlier papers we have constructed difference methods that are fourth-order accurate both in space and time for wave propagation problems. The analysis and numerical experiments have been limited to one-dimensional problems. In this paper we extend the construction and the analysis to two space dimensions, and present numerical experiments for acoustic problems in discontinuous media.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76M20 Finite difference methods applied to problems in fluid mechanics
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[1] Brown, D., A note on the numerical solution of the wave equation with piecewise smooth coefficients, Math. Comp., 42, 369-391 (1984) · Zbl 0558.65072 · doi:10.2307/2007591
[2] Carpenter, M.; Gottlieb, D.; Abarabanel, S.; Don, W.-S., The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: a study of the boundary error, SIAM J. Sci. Comput., 16, 1241-1252 (1995) · Zbl 0839.65098 · doi:10.1137/0916072
[3] Cohen, G.; Joly, P., Construction and analysis of fourth-order finite difference schemes for the acoustic wave equation in nonhomogeneous media, SIAM J. Numer. Anal., 33, 1266-1302 (1996) · Zbl 0863.65048 · doi:10.1137/S0036142993246445
[4] Gustafsson, B.; Kreiss, H.-O.; Oliger, J., Time Dependent Problems and Difference Methods (1995), Boston: Wiley, Boston · Zbl 0843.65061
[5] Gustafsson, B.; Mossberg, E., Time compact high order difference methods for wave propagation, SIAM J. Scient. Comp., 26, 259-271 (2004) · Zbl 1075.65112 · doi:10.1137/030602459
[6] Gustafsson, B.; Wahlund, P., Time compact difference methods for wave propagation in discontinuous media, SIAM J. Scient. Comp., 26, 272-293 (2004) · Zbl 1077.65092 · doi:10.1137/S1064827503425900
[7] Lax, P. D.; Wendroff, B., Difference schemes for hyperbolic equations with high order accuracy, Comm. Pure Appl. Math., 17, 381-398 (1964) · Zbl 0233.65050 · doi:10.1002/cpa.3160170311
[8] Noumerov, B. V., A method of extrapolation of perturbations, Monthly Notices Roy. Astronom. Soc., 84, 592-601 (1924)
[9] Numerov, B., Note on the numerical integration ofd^2x/dt^2 =f(x, t), Astronom. Nachr., 230, 359-364 (1927) · JFM 53.0526.03 · doi:10.1002/asna.19272301903
[10] Reddy, S.; Trefethen, L., Stability of the method of lines, Num. Math., 62, 235-267 (1992) · Zbl 0734.65077 · doi:10.1007/BF01396228
[11] Shubin, G. R.; Bell, J., A modified equation approach to constructing fourth order methods for acoustic wave propagation, SIAM J. Sci. Stat. Comput., 8, 135-151 (1987) · Zbl 0611.76091 · doi:10.1137/0908026
[12] Yee, K., Numerical solution of intial boundary value problems involving Maxwell’s equations in isotropic media, IEEE Trans. Antennas and Prop., 14, 302-307 (1966) · Zbl 1155.78304 · doi:10.1109/TAP.1966.1138693
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