Geodesic
A nonlocal problem for singular linear systems of ordinary differential equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 7, pp. 1228-1235 
A. A. Abramov; V. I. Ul'yanova; L. F. Yukhno. A nonlocal problem for singular linear systems of ordinary differential equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 7, pp. 1228-1235. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_7_a4/
@article{ZVMMF_2011_51_7_a4,
     author = {A. A. Abramov and V. I. Ul'yanova and L. F. Yukhno},
     title = {A~nonlocal problem for singular linear systems of ordinary differential equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1228--1235},
     year = {2011},
     volume = {51},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_7_a4/}
}
TY  - JOUR
AU  - A. A. Abramov
AU  - V. I. Ul'yanova
AU  - L. F. Yukhno
TI  - A nonlocal problem for singular linear systems of ordinary differential equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2011
SP  - 1228
EP  - 1235
VL  - 51
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_7_a4/
LA  - ru
ID  - ZVMMF_2011_51_7_a4
ER  - 
%0 Journal Article
%A A. A. Abramov
%A V. I. Ul'yanova
%A L. F. Yukhno
%T A nonlocal problem for singular linear systems of ordinary differential equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2011
%P 1228-1235
%V 51
%N 7
%U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_7_a4/
%G ru
%F ZVMMF_2011_51_7_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

A system of linear ordinary differential equations is examined on an infinite half-interval. This system is supplemented by the boundedness condition for solutions and a nonlocal linear condition specified by the Stieltjes integral. A method for approximating the resulting problem by a problem posed on a finite interval is proposed, and the properties of the latter are investigated. A numerically stable method for solving this problem is examined. This method uses an auxiliary boundary value problem with separated boundary conditions.

[1] Abramov A. A., Konyukhova N. B., “Transfer of admissible boundary conditions from a singular point for systems of linear ordinary differential equations”, Sovjet. J. Numer. Analys. Math. Modelling, 1:4 (1986), 245–265 | DOI | MR | Zbl

[2] Abramov A. A., Andreev B. V., “O primenenii metoda progonki k nakhozhdeniyu periodicheskikh reshenii differentsialnykh i raznostnykh uravnenii”, Zh. vychisl. matem. i matem. fiz., 3:2 (1963), 377–381 | MR | Zbl

[3] Dzhangirova S. A., “O mnogotochechnykh zadachakh dlya sistem obyknovennykh differentsialnykh uravnenii”, Zh. vychisl. matem. i matem. fiz., 27:9 (1987), 1375–1380 | MR

[4] Abramov A. A., “O perenose granichnykh uslovii dlya sistem lineinykh obyknovennykh differentsialnykh uravnenii (variant metoda progonki)”, Zh. vychisl. matem. i matem. fiz., 1:3 (1961), 542–545 | MR | Zbl

[5] Abramov A. A., “O chislennoi ustoichivosti odnogo metoda perenosa granichnykh uslovii”, Zh. vychisl. matem. i matem. fiz., 46:3 (2006), 401–406 | MR | Zbl