Geodesic
Family of fifth-order three-level schemes for evolution problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 2, pp. 206-221 Cet article a éte moissonné depuis la source Math-Net.Ru

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A multiparameter family of fifth-order three-level schemes in time based on compact approximations is presented for solving evolution problems. The schemes are adapted to hyperbolic and parabolic equations and to stiff systems of ordinary differential equations. In the case of hyperbolic equations, a fifth-order accurate scheme in all variables with compact approximations of spatial derivatives is analyzed. Stability estimates are presented, and the dispersive and dissipative properties are examined. 
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A. I. Tolstykh. Family of fifth-order three-level schemes for evolution problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 2, pp. 206-221. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_2_a1/

[1] Tolstykh A. I., Kompaktnye raznostnye skhemy i ikh primenenie v zadachakh aerogidrodinamiki, Nauka, M., 1990 | MR

[2] Tolstykh A. I., “Two-step fifth-order methods for evolutionary problems with positive operators”, Positivity, 2 (1998), 193–219 | DOI | MR | Zbl

[3] Tolstykh A. I., “Ob odnom klasse netsentrirovannykh kompaktnykh skhem pyatogo poryadka, osnovannom na approksimatsiyakh Pade”, Dokl. RAN, 326:1 (1991), 72–77 | MR

[4] Lipavskii M. V., Tolstykh A. I., “O sravnitelnoi effektivnosti skhem s netsentrirovannymi kompaktnymi approksimatsiyami”, Zh. vychisl. matem. i matem. fiz., 39:10 (1999), 1705–1720 | MR

[5] Enright W. H., “Second derivative multistep methods for stiff ordinary differential equations”, SIAM J. Numer. Analys., 11:2 (1974), 321–331 | DOI | MR | Zbl

[6] Hall Cr. (ed.), Modern numerical methods for ordinary differential equation, Clarendon Press, Oxford, 1976 | MR | Zbl

[7] Dekker K., Verwer J. G., Stability of Runge–Kutta methods for stiff nonlinear differential equations, North-Holland, Amsterdam. etc., 1984 | MR | Zbl

[8] Godunov S. K., Ryabenkii V. S., Raznostnye skhemy, Nauka, M., 1973 | Zbl