Geodesic
Finite-difference schemes for solving multidimensional hyperbolic equations and their systems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 6, pp. 980-987 Cet article a éte moissonné depuis la source Math-Net.Ru

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A numerical algorithm for integrating second-order multidimensional hyperbolic equations and hyperbolic systems is described. Conditionally and unconditionally stable finite-difference schemes are constructed. The analysis of the schemes is based on the general regularization principle proposed by A. A. Samarskii. 
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O. P. Komurdzhishvili. Finite-difference schemes for solving multidimensional hyperbolic equations and their systems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 6, pp. 980-987. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_6_a4/

[1] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1977 | MR | Zbl

[2] Yanenko H.Ḣ., Metod drobnykh shagov resheniya mnogomernykh zadach matematicheskoi fiziki, Nauka, Novosibirsk, 1967

[3] Marchuk G. I., Metody vychislitelnoi matematiki, Nauka, M., 1977 | MR | Zbl

[4] Samarskii A. A., “O regulyarizatsii raznostnykh skhem”, Zh. vychisl. matem. i matem. fiz., 7:1 (1967), 62–93 | MR

[5] Samarskii A. A., “Klassy ustoichivykh skhem”, Zh. vychisl. matem. i matem. fiz., 7:5 (1967), 1096–1133 | MR