The application of a spinor calculus to the investigation of the stability of finite-difference schemes
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 43 (2003) no. 2, pp. 235-250 Cet article a éte moissonné depuis la source Math-Net.Ru

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E. V. Vorozhtsov; B. Yu. Skobelev. The application of a spinor calculus to the investigation of the stability of finite-difference schemes. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 43 (2003) no. 2, pp. 235-250. http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_2_a7/

[1] Rikhtmaier R., Morton K., Raznostnye metody resheniya kraevykh zadach, Mir, M., 1972

[2] Samarskii A. A., Gulin A. V., Ustoichivost raznostnykh skhem, Nauka, M., 1973 | Zbl

[3] Samarskii A. A., Teoriya raznostnykh skhem, 3-e izd., Nauka, M., 1989 | MR

[4] Gustafsson B., Kreiss H.-O., Oliger J., Time dependent problems and difference methods, Wiley, New York, 1995 | MR

[5] Levy D., Tadmor E., “From semidiscrete to fully discrete stability of Runge–Kutta schemes by the energy method”, SIAM Rev., 40:1 (1998), 40–73 | DOI | MR | Zbl

[6] Samarskii A. A., Vabischevich P. N., “Nelineinye monotonnye skhemy dlya uravneniya perenosa”, Dokl. RAN, 361:1 (1998), 21–23 | MR

[7] Samarskii A. A., Vabischevich P. N., Additivnye skhemy dlya zadach matematicheskoi fiziki, Nauka, M., 1999 | MR

[8] Samarskii A. A., Vabischevich P. N., Chislennye metody resheniya zadach konvektsii-diffuzii, Editorial URSS, M., 1999

[9] Vabischevich P. N., Samarskii A. A., “Raznostnye skhemy dlya zadach konvektsii-diffuzii na neregulyarnykh setkakh”, Zh. vychisl. matem. i matem. fiz., 40:5 (2000), 726–739 | MR

[10] Vabischevich P. N., Pervichko V. A., Samarskii A. A., Chudanov V. V., “Nelineinye regulyarizovannye raznostnye skhemy dlya mnogomernogo uravneniya perenosa”, Zh. vychisl. matem. i matem. fiz., 40:6 (2000), 900–907 | MR

[11] Pinchukov V. I., Shu Ch.-V., Chislennye metody vysokikh poryadkov dlya zadach aerogidrodinamiki, Izd-vo SO RAN, Novosibirsk, 2000

[12] Mazhukin V. I., Malafei D. A., Matus P. P., Samarskii A. A., “Raznostnye skhemy na neravnomernykh setkakh dlya uravnenii matematicheskoi fiziki s peremennymi koeffitsientami”, Zh. vychisl. matem. i matem. fiz., 41:3 (2001), 407–419 | MR | Zbl

[13] Strikwerda J. C., Finite difference schemes and partial differential equations, Wadsworth Brooks, Pacific Grove, CA; Cole Advanced Books Software, 1989 | MR | Zbl

[14] Godunov C. K., Ryabenkii B. C., Raznostnye skhemy. Vvedenie v teoriyu, Nauka, M., 1977 | MR

[15] Scobelev B. Yu., “On the question about the sufficiency of the von Neumann criterion for stability of difference schemes”, J. Comput. Phys., 143:1 (1998), 278–282 | DOI | MR

[16] Scobelev B. Yu., Vorozhtsov E. V., “Sufficient stability criteria and uniform stability of difference schemes”, J. Comput. Phys., 165:2 (2000), 717–751 | DOI | MR | Zbl

[17] Zhelnorovich V. A., Teoriya spinorov i ee primenenie v fizike i mekhanike, Nauka, M., 1982 | MR | Zbl

[18] Dirak P., Printsipy kvantovoi mekhaniki, Izd. 2-e, Nauka, M., 1979 | MR

[19] Lounesto P., Clifford algebras and spinors, Cambridge Univ. Press, Cambridge, UK, 1997 | MR | Zbl

[20] Van der Varden B. L., Algebra, Nauka, M., 1976 | MR

[21] Godunov S. K., Mikhailova T. Yu., Predstavleniya gruppy vraschenii i sfericheskie funktsii, Nauchn. kniga, Novosibirsk, 1998 | MR

[22] Bogolyubov N. N., Shirkov D. V., Vvedenie v teoriyu kvantovannykh polei, Izd. 2-e, Nauka, M., 1973 | MR | Zbl

[23] MacCormack R. W., The effect of viscosity in hypervelocity impact cratering, AIAA Paper No 354, 1969

[24] Vorozhtsov E. V., Scobelev B. Yu., Ganzha V. G., “Symbolic-numerical method for the stability analysis of difference schemes on the basis of the catastrophe theory”, J. Comput. Phys., 116:1 (1995), 26–38 | DOI | MR | Zbl

[25] Wendroff B., “The stability of MacCormack's method for the scalar advection equation”, Appl. Math. Letts., 4:1 (1991), 89–91 | DOI | MR | Zbl

[26] Vorozhtsov E. V., Scobelev B. Yu., Ganzha V. G., “Symbolic-numerical method for the stability analysis of difference schemes on the basis of the catastrophe theory. Corrigendum”, J. Comput. Phys., 123:1 (1996), 231–232 | DOI | MR | Zbl

[27] Hong H., “The exact stability region of the MacCormack scheme for scalar advection equation”, Appl. Math. Letts., 9:4 (1996), 99–101 | DOI | Zbl

[28] LeVeque R. J., Numerical methods for conservation laws, Birkhäuser, Basel, 1992 | MR | Zbl

[29] Harten A., “High resolution schemes for hyperbolic conservation laws”, J. Comput. Phys., 49:3 (1983), 357–393 | DOI | MR | Zbl

[30] Zang T. A., Krist S. E., Hussaini M. Y., “Resolution requirements for numerical simulations of transition”, Lect. Notes Engng., no. 3, 1988, 508–525 | MR

[31] Fletcher K., Vychislitelnye metody v dinamike zhidkostei, v. 1, 2, Mir, M., 1991