Geodesic
A relationship between order and degree for a stable formula with advanced nodes
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 7, pp. 1045-1056 
V. R. Ibragimov. A relationship between order and degree for a stable formula with advanced nodes. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 7, pp. 1045-1056. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_7_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A major problem in the implementation of $k$-step methods is to determine their accuracy. This problem is solved using relationships between order and degree for a $k$-step method. A relationship between order and degree is found for stable multistep methods with a second derivative.

[1] Bakhvalov N. S., “Nekotorye zamechaniya k voprosu o chislennom integrirovanii differentsialnykh uravnenii metodom konechnykh raznostei”, Dokl. AN SSSR, 104:6 (1955), 805–808 | Zbl

[2] Dahlquist G., “Convergence and stability in the numerical integration of ordinary differential equations”, Math. Scand., 4:1 (1956), 33–53 | MR | Zbl

[3] Ibragimov V. P., “Odin nelineinyi metod chislennogo resheniya zadachi Koshi dlya obyknovennykh differentsialnykh uravnenii”, Differents. ur-niya i primeneniya, Tr. II Vses. konf. (Russe, Bolgariya, 1981), Russe, Bolgariya, 1982, 310–319 | Zbl

[4] Bakhvalov N. S., Chislennye metody, Nauka, M., 1978 | MR | Zbl

[5] Ibragimov V. R., “Svyaz mezhdu poryadkom i stepenyu ustoichivoi raznostnoi formuly s zabeganiem vpered”, Priblizhennye metody operatornykh ur-nii, Azgosuniversitet, Baku, 1984, 55–63 | MR

[6] Ibragimov V. R., “Skhodimost metoda prognoza-korrektsii”, Godishnik na visshite uchebni zavedeniya: Prilozhna matem., 20:4 (1984), 187–197 | MR