Geodesic
Approximation of the solutions of exponentially stable difference-differential equations
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2011), pp. 29-38
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The algorithm of approximation of the domain of asymptotic stability of stationary system of difference-differential equations is developed. This approximation is based on the construction of the domain of asymptotic stability of corresponding difference schemes. The method is based on Adams scheme approximation of the solutions of difference-differential system with a delay. This system allows for exponentially stable linear approximation represented by the system of difference equations. The example illustrating feasibility of this approach is presented.
Keywords: exponentially stable, difference-differential system, difference approximation, the domain of asymptotic stability. 
@article{VSPUI_2011_3_a3,
     author = {A. P. Zhabko and U. P. Zaranik},
     title = {Approximation of the solutions of exponentially stable difference-differential equations},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {29--38},
     year = {2011},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2011_3_a3/}
}
TY  - JOUR
AU  - A. P. Zhabko
AU  - U. P. Zaranik
TI  - Approximation of the solutions of exponentially stable difference-differential equations
JO  - Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
PY  - 2011
SP  - 29
EP  - 38
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VSPUI_2011_3_a3/
LA  - ru
ID  - VSPUI_2011_3_a3
ER  - 
%0 Journal Article
%A A. P. Zhabko
%A U. P. Zaranik
%T Approximation of the solutions of exponentially stable difference-differential equations
%J Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
%D 2011
%P 29-38
%N 3
%U http://geodesic.mathdoc.fr/item/VSPUI_2011_3_a3/
%G ru
%F VSPUI_2011_3_a3
A. P. Zhabko; U. P. Zaranik. Approximation of the solutions of exponentially stable difference-differential equations. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2011), pp. 29-38. http://geodesic.mathdoc.fr/item/VSPUI_2011_3_a3/

[1] Krasovskii N. N., “O primenenii vtorogo metoda Lyapunova dlya uravnenii s zapazdyvaniem vremeni”, Prikladnaya matematika i mekhanika, 20 (1956), 315–327

[2] Kharitonov V. L., “Funktsionaly Lyapunova s zadannoi proizvodnoi. I. Funktsionaly polnogo tipa”, Vestn. S.-Peterb. un-ta. Ser. 10: Prikladnaya matematika, informatika, protsessy upravleniya, 2005, no. 1, 110–117

[3] Letyagina O. N., Zhabko A. P., “Robust stability analysis of linear periodic system with time delay”, Intern. journal of modern physics A, 24:5 (2009), 893–907 | DOI | Zbl

[4] Zhabko A. P., Zaranik U. P., “Ob odnom sposobe priblizheniya oblasti asimptoticheskoi ustoichivosti differentsialno-raznostnykh sistem”, Vestn. Mordov. un-ta. Ser. Fiziko-matematicheskie nauki, 2011, no. 1, 43–48

[5] Buzlukova Yu. A., “Oblast asimptoticheskoi ustoichivosti reshenii sistem differentsialno-raznostnykh uravnenii”, Trudy Srednevolzhsk. matem. ob-va, 6:1 (2004), 204–215

[6] Zaranik U. P., “Postroenie oblasti asimptoticheskoi ustoichivosti raznostnykh sistem”, Vestn. S.-Peterb. un-ta. Ser. 10: Prikladnaya matematika, informatika, protsessy upravleniya, 2005, no. 2, 11–15 | MR

[7] Bellman R., Kuk K., Differentsialno-raznostnye uravneniya, per. s angl. A. M. Zverkina, G. A. Kamenskogo, ed. L. E. Eltsgolts, Mir, M., 1967, 548 pp.

[8] Bakhvalov N. S., Zhidkov N. P., Kobelkov G. M., Chislennye metody, Nauka, M., 1987, 600 pp.