Geodesic
The stability boundaries of difference schemes on nonuniform grids
Matematičeskoe modelirovanie, Tome 17 (2005) no. 11, pp. 85-92.

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In this paper we consider the problem of dependence of the stability boundary of difference schemes relately to nonuniform grids. We investigate grids having the nonuniformity only at the ends of segment, i.e. the grids with two and three different mesh sizes. It is shown that there exist nonuniform grids for which the difference schemes have a little more stability reserve than in the case of uniform grids having the same number of nodes. 
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V. P. Ilyutko. The stability boundaries of difference schemes on nonuniform grids. Matematičeskoe modelirovanie, Tome 17 (2005) no. 11, pp. 85-92. http://geodesic.mathdoc.fr/item/MM_2005_17_11_a6/

[1] Samarskii A. A., Gulin A. V., “Kriterii ustoichivosti semeistva raznostnykh skhem”, DAN, 330:6 (1993), 694–695 | MR

[2] Gulin A. V., Samarskii A. A., “Ob ustoichivosti odnogo klassa raznostnykh skhem”, Differentsialnye uravneniya, 29:7 (1993), 1163–1174 | MR

[3] Samarskii A. A., Vabischevich P. N., Gulin A. V., “Ustoichivost operatorno-raznostnykh skhem”, Differentsialnye uravneniya, 35:2 (1999), 152–187 | MR

[4] Gulin A. V., Degtyarev S. L., “Kriterii ustoichivosti dvumernoi raznostnoi skhemy”, Differentsialnye uravneniya, 32:7 (1996), 943–950 | MR | Zbl

[5] Samarskii A. A., Gulin A. V., Vukoslavchevich V., “Kriterii ustoichivosti dvusloinykh i trekhsloinykh raznostnykh skhem”, Differentsialnye uravneniya, 34:7 (1998), 975–979 | MR

[6] Gulin A. V., Gulin V. A., “Granitsy ustoichivosti raznostnykh skhem s peremennymi vesovymi mnozhitelyami”, Izvestiya vuzov. Matematika, 1994, no. 9(388), 28–38 | MR | Zbl

[7] Gulin A. V., Sheredina A. V., “Granitsy ustoichivosti raznostnykh skhem”, Izvestiya vuzov. Matematika, 2000, no. 11, 26–33 | MR | Zbl

[8] Tikhonov A. N., Samarskii A. A., “Odnorodnye raznostnye skhemy na neravnomernykh setkakh”, ZhVM i MF, 2:5 (1962), 812–832 | MR | Zbl

[9] Samarskii A. A., Teoriya raznostnykh skhem, 3-e izd., Nauka, M., 1989, 616 pp. | MR

[10] Kalitkin N. N., Chislennye metody, Nauka, M., 1968, 512 pp. | MR

[11] Samarskii A. A., Andreev V. B., Raznostnye metody dlya ellipticheskikh uravnenii, Nauka, M., 1976, 352 pp. | MR | Zbl