Geodesic
On the strong monotonicity of nonlinear difference schemes
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 38 (1998) no. 7, pp. 1170-1185 Cet article a éte moissonné depuis la source Math-Net.Ru

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V. V. Ostapenko. On the strong monotonicity of nonlinear difference schemes. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 38 (1998) no. 7, pp. 1170-1185. http://geodesic.mathdoc.fr/item/ZVMMF_1998_38_7_a12/

[1] Lax P. D., Hyperbolic systems of conservation laws and the mathematical theory of shock waves, Soc. Industr. and Appl. Math., Philadelphia, 1972 | Zbl

[2] Rozhdestvenskii B. L., Yanenko N. N., Sistemy kvazilineinykh uravnenii, Nauka, M., 1978

[3] Voevodin A. F., Shugrin S. M., Metody resheniya odnomernykh evolyutsionnykh sistem, Nauka, Novosibirsk, 1993

[4] Samarskii A. F., Popov Yu. P., Raznostnye metody resheniya zadach gazovoi dinamiki, Nauka, M., 1980

[5] Kolgan V. P., “Primenenie printsipa minimalnykh znachenii proizvodnoi k postroeniyu konechno-raznostnykh skhem dlya rascheta razryvnykh reshenii gazovoi dinamiki”, Uch. zap. TsAGI, 3:6 (1972), 68–78

[6] Van Leer B., “Towards the ultimate conservative difference scheme. V. A second order sequel to Godunov's methods”, J. Comput. Phys., 32:1 (1979), 101–136 | DOI

[7] Harten A., “A High resolution schemes for hyperbolic conservation laws”, J. Comput. Phys., 49 (1983), 357–393 | DOI | MR | Zbl

[8] Roe P. L., “Some contributions to the modelling of discontinuous flows”, Lect. Appl. Math., 22:2 (1985), 163–195 | MR

[9] Anderson W. K., Thomas J. L., van Leer B., “Comparison of finite volume flux vector splitings for the Euler equations”, AIAA J., 24:9 (1986), 1453–1460 | DOI

[10] Rodionov A. B., “Povyshenie poryadka approksimatsii skhemy S. K. Godunova”, Zh. vychisl. matem. i matem. fiz., 27:12 (1987), 1853–1860 | MR | Zbl

[11] Harten A., Osher S., “Uniformly high-order accurate nonoscillatory scheme”, SIAM J. Numer. Analys., 24:2 (1987), 279–309 | DOI | MR | Zbl

[12] Shu C. W., “TVB uniformly high order schemes for conservation laws”, Math. Comput., 49:179 (1987), 105–121 | DOI | Zbl

[13] Vyaznikov K. B., Tishkin V. F., Favorskii A. P., “Postroenie monotonnykh raznostnykh skhem povyshennogo poryadka approksimatsii dlya sistem uravnenii giperbolicheskogo tipa”, Matem. modelirovanie, 1:5 (1989), 95–120 | MR | Zbl

[14] Vila J. P., “An analysis of a class of second-order accurate Godunov-type schemes”, SIAM J. Numer. Analys., 26:4 (1989), 830–853 | DOI | MR | Zbl

[15] Pinnukov V. I., “O postroenii monotonnykh skhem tipa prediktor-korrektor proizvolnogo poryadka approksimatsii”, Matem. modelirovanie, 3:9 (1991), 95–103 | MR

[16] Ilin S. A., Timofeev E. V., “Sravnenie kvazimonotonnykh raznostnykh skhem skvoznogo scheta na zadache Koshi dlya odnomernogo lineinogo uravneniya perenosa”, Matem. modelirovanie, 4:3 (1992), 62–75

[17] Godunov S. K., “Raznostnyi metod chislennogo rascheta razryvnykh reshenii uravnenii gidrodinamiki”, Matem. sb., 47:3 (1959), 271–306 | MR | Zbl

[18] Lax P. D., “Weak solutions of nonlinear hyperbolic equations and their numerical computation”, Communs Pure and Appl. Math., 7 (1954), 159–193 | DOI | MR | Zbl

[19] Roe P. L., “Sonic flux formulae”, SIAM J. Sci. Statist. Comput., 13:2 (1992), 611–630 | DOI | MR | Zbl

[20] Ostapenko V. V., “O skhodimosti raznostnykh skhem za frontom nestatsionarnoi udarnoi volny”, Zh. vychisl. matem. i matem. fiz., 37:10 (1987), 1201–1212 | MR

[21] Arora M., Roe P. L., “On postshock oscillations due to shock cap taring schemes in unsteady flows”, J. Comput Phys., 130 (1997), 25–40 | DOI | MR | Zbl