Geodesic
Stability of difference schemes in terms of Riemann invariants for a polytropic gas
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 6, pp. 1078-1091

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The monotonicity and stability of a finite difference scheme with respect to initial data in the supremum norm are analyzed as applied to the polytropic gas equations written in terms of Riemann invariants for subsonic flows with $1\gamma3$. Conditions on the initial and boundary data are obtained under which subsonic flows with no shock waves develop in the medium. The theoretical conclusions are supported by numerical results. 
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     title = {Stability of difference schemes in terms of {Riemann} invariants for a polytropic gas},
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G. L. Martsinkevich; P. P. Matus; M. M. Chuǐko. Stability of difference schemes in terms of Riemann invariants for a polytropic gas. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 6, pp. 1078-1091. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_6_a8/