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On the monotonicity of multidimensional difference schemes. (English. Russian summary) Zbl 1264.65139
Dokl. Math. 86, No. 3, 766-769 (2012); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 447, No. 2, 146-149 (2012).
The author extends the concept of monotone difference scheme to the multidimensional case. The main result of the paper establishes that the difference scheme algorithm is monotone if and only if the coefficients are nonnegative.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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[1] P. D. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves (SIAM, Philadelphia, 1972).
[2] B. L. Rozhdestvenskii and N. N. Yanenko, Systems of Quasilinear Equations and Their Applications to Gas Dynamics (Nauka, Moscow, 1978).
[3] A. G. Kulikovskii, N. V. Pogorelov, and A. Yu. Semenov, Mathematical Aspects of Numerical Solution of Hyperbolic Systems (Fizmatlit, Moscow, 2001; Chapman and Hall/CRC, London, 2001). · Zbl 0965.35001
[4] V. V. Ostapenko, Hyperbolic Systems of Conservation Laws and Their Applications to Shallow Water Theory (Novosib. Gos. Univ., Novosibirsk, 2004) [in Russian].
[5] S. K. Godunov, Mat. Sb. 47, 271–306 (1959).
[6] A. Harten, J. M. Hyman, and R. D. Lax, Commun. Pure Appl. Math. 29, 297–322 (1976). · Zbl 0351.76070 · doi:10.1002/cpa.3160290305
[7] L. Abrahamsson and S. Osher, SIAM J. Numer Anal. 19, 979–992 (1982). · Zbl 0507.65039 · doi:10.1137/0719071
[8] A. S. Kholodov, USSR Comput. Math. Math. Phys. 20(6), 234–253 (1980). · Zbl 0477.65065 · doi:10.1016/0041-5553(80)90017-8
[9] K. V. Vyazniko, V. F. Tishkin, and A. P. Favorskii, Mat. Model. 1(5), 95–120 (1989).
[10] P. A. Forsyth and M. C. Kropinnski, SIAM J. Sci. Comput. 18, 1328–1354 (1997). · Zbl 0897.76048 · doi:10.1137/S1064827594265824
[11] V. S. Borisov and S. Sorek, SIAM J. Sci. Comput. 25, 1557–1584 (2004). · Zbl 1133.35327 · doi:10.1137/S1064827502406695
[12] A. A. Harten, J. Comp. Phys. 49, 357–393 (1983). · Zbl 0565.65050 · doi:10.1016/0021-9991(83)90136-5
[13] V. V. Ostapenko, Sib. Math. J. 39, 959–972 (1998); 1174–1183 (1998). · Zbl 0916.65093 · doi:10.1007/BF02672918
[14] X. Liu and E. Tadmor, Numer. Math. 79, 397–425 (1998). · Zbl 0906.65093 · doi:10.1007/s002110050345
[15] V. V. Ostapenko, Comput. Math. Math. Phys. 38, 1119–1133 (1998); 39, 1619–1635 (1999).
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