Geodesic
On sufficient conditions of stability in explicit scheme S. K. Godunov
Matematičeskoe modelirovanie, Tome 17 (2005) no. 12, pp. 119-128 Cet article a éte moissonné depuis la source Math-Net.Ru

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Sufficient stability conditions for explicit difference schemes approximating in conservative (divergent) way the unsteady conservation laws of gas dynamics were developed by the author earlier. In this paper it is shown that these conditions can be made less strong for divergent schemes using three nodes with respect to every space coordinate. 
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V. G. Grudnitskii. On sufficient conditions of stability in explicit scheme S. K. Godunov. Matematičeskoe modelirovanie, Tome 17 (2005) no. 12, pp. 119-128. http://geodesic.mathdoc.fr/item/MM_2005_17_12_a5/

[1] V. G. Grudnitskii, “Obobschënnye kharakteristiki dlya sistemy uravnenii Eilera i ikh primenenie k konstruirovaniyu chislennykh skhem”, Mat. modelirovanie, 4:12 (1992), 45–48

[2] V. G. Grudnitskii, “Obobschënnye kharakteristiki dlya sistemy uravnenii Eilera”, Algoritmy dlya chislennogo issledovaniya razryvnykh techenii, VTs RAN, 1993, 191–203 | MR

[3] V. G. Grudnitskii, “Obobschënnye kharakteristiki i dostatochnoe uslovie ustoichivosti dlya uravnenii Eilera s razryvnymi resheniyami”, Mat. modelirovanie, 9:12 (1997), 121–125 | MR

[4] V. G. Grudnitskii, “Dostatochnoe uslovie ustoichivosti pri yavnom postroenii razryvnykh reshenii sistemy uravnenii Eilera”, Dok. Akademii nauk, 362:3 (1998), 298–299 | MR

[5] V. G. Grudnitskii, “Dostatochnoe uslovie ustoichivosti mnogomernogo raschëta nestatsionarnykh razryvnykh reshenii uravnenii Eilera”, Mat. modelirovanie, 12:1 (2000), 65–77 | MR

[6] V. G. Grudnitskii, P. V. Plotnikov, “Obobschënnye kharakteristiki i dostatochnoe uslovie ustoichivosti pri postroenii razryvnykh reshenii sistemy uravnenii Eilera”, Novoe v chislennom modelirovanii, 2000, 148–164 | MR

[7] V. G. Grudnitskiy, “Sufficient conditions of stability for discontinuous solutions of the Euler equations”, Computational Fluid Dynamics JOURNAL, 10:2 (2001), 334–337

[8] V. G. Grudnitskii, “Pryamoi obobschënno-kharakteristicheskii metod dlya raschëta razryvnykh reshenii zakonov sokhraneniya gazovoi dinamiki”, Mat. modelirovanie, 16:1 (2004), 90–96 | MR | Zbl

[9] V. G. Grudnitskii, “O povedenii chislennogo resheniya kraevykh zadach dlya evolyutsionnykh uravnenii v bolshikh oblastyakh”, Dok. Akademii nauk, 252:5 (1980), 1041–1044 | MR

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

[11] S. K. Godunov, “Raznostnyi metod raschëta udarnoi volny”, UMN, 12:1(73) (1957), 176–177 | MR | Zbl

[12] B. L. Rozhdestvenskii, N. N. Yanenko, Sistemy kvazilineinykh uravnenii, Nauka, Moskva, 1978 | MR