Geodesic
Solving a~system of differential equations of block structure with unseparated boundary conditions
Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 4, pp. 3-13.

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

We study the solution of a system of higher-dimensional ordinary differential equations of block structure. Separate subsystems are connected with each other by unseparated boundary conditions caused by an arbitrary relation between the boundary values of the solutions to the subsystems. For numerical solution, we propose a scheme of the method of transfer of boundary conditions taking into account some specific characteristics of systems under consideration. The results of numerical experiments are given.
Keywords: system of differential equations, block structure of the system, unseparated boundary condition, method of transfer of conditions, Cauchy problem, Runge–Kutta method. 
@article{SJIM_2014_17_4_a0,
     author = {K. R. Aida-zade and Y. R. Ashrafova},
     title = {Solving a~system of differential equations of block structure with unseparated boundary conditions},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {3--13},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2014_17_4_a0/}
}
TY  - JOUR
AU  - K. R. Aida-zade
AU  - Y. R. Ashrafova
TI  - Solving a~system of differential equations of block structure with unseparated boundary conditions
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2014
SP  - 3
EP  - 13
VL  - 17
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2014_17_4_a0/
LA  - ru
ID  - SJIM_2014_17_4_a0
ER  - 
%0 Journal Article
%A K. R. Aida-zade
%A Y. R. Ashrafova
%T Solving a~system of differential equations of block structure with unseparated boundary conditions
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2014
%P 3-13
%V 17
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2014_17_4_a0/
%G ru
%F SJIM_2014_17_4_a0
K. R. Aida-zade; Y. R. Ashrafova. Solving a~system of differential equations of block structure with unseparated boundary conditions. Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 4, pp. 3-13. http://geodesic.mathdoc.fr/item/SJIM_2014_17_4_a0/

[1] Tsurkov V. I., Dekompozitsiya v zadachakh bolshoi razmernosti, Nauka, M., 1981 | MR | Zbl

[2] Yanushevskii R. T., “Dekompozitsiya pri reshenii optimalnykh zadach sinteza lineinykh mnogosvyaznykh sistem upravleniya”, Teoriya i metody postroeniya sistem mnogosvyaznogo regulirovaniya, Nauka, M., 1973, 144–150

[3] Aida-zade K. R., “Issledovanie i chislennoe reshenie konechno-raznostnykh approksimatsii zadach upravleniya sistemami s raspredelennymi parametrami”, Zhurn. vychisl. matematiki i mat. fiziki, 29:3 (1989), 346–354 | MR | Zbl

[4] Aida-zade K. R., Ali-zade R. I., Novruzbekov I. G., Kalaushin M. A., “Dekompozitsionnyi metod analiza i sinteza ploskikh mekhanizmov”, Mekhanika mashin, 57, 1980, 26–30

[5] Aida-zade K. R., “Investigation of non-linear optimization problems of networks structure”, Automation and Remote Control, 51:2 (1990), 135–145 | MR | Zbl

[6] Voronov A. A., Vvedenie v dinamiku slozhnykh upravlyaemykh sistem, Nauka, M., 1985 | MR

[7] Krasovskii A. A., “Dekompozitsiya i sintez suboptimalnykh adaptivnykh sistem”, Izv. AN SSSR. Ser. Tekhn. kibernetika, 1984, no. 2, 157–165 | MR

[8] Efendiev Y., Galvis J., Lazarov R. D., Margenov S., Ren J., Multiscale domain decomposition preconditioners for anisotropic high-contrast problems, Technical Report ISC-Preprint 2011-05, Institute for Scientific Computation, 2011

[9] Geiser J., Decomposition methods for differential equations: theory and applications, CRC Press, Taylor and Francis Group, 2009 | MR | Zbl

[10] Abramov A. A., “O perenose granichnykh uslovii dlya sistem lineinykh obyknovennykh differentsialnykh uravnenii (variant metoda progonki)”, Zhurn. vychisl. matematiki i mat. fiziki, 1:3 (1961), 542–545 | MR | Zbl

[11] Abramov A. A., Burago N. G., Dyshko A. L. i dr., “Paket prikladnykh programm dlya resheniya lineinykh dvukhtochechnykh kraevykh zadach”, Soobscheniya po programmnomu obespecheniyu EVM, izd. VTs AN SSSR, M., 1982

[12] Abdullaev V. M., “Reshenie differentsialnykh uravnenii s nerazdelennymi mnogotochechnymi i integralnymi usloviyami”, Sib. zhurn. industr. matematiki, 15:3 (2012), 3–15 | MR

[13] Aida-zade K. R., Abdullaev V. M., “Zadacha upravleniya s nerazdelennymi mnogotochechnymi i integralnymi usloviyami”, Problemy upravleniya i informatiki, 2013, no. 2, 61–77

[14] Aida-zade K. R., Abdullaev V. M., “On the solution of boundary value problems with nonseparated multipoint and integral conditions”, Differential Equations, 49:9 (2013), 1114–1125 | DOI | MR | Zbl

[15] Godunov S. K., Ryabenkii V. S., Vvedenie v teoriyu raznostnykh skhem, Fizmatgiz, M., 1962 | MR

[16] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1983 | MR

[17] Samarskii A. A., Nikolaev E. S., Metody resheniya setochnykh uravnenii, Nauka, M., 1978 | MR

[18] Tamarkin Ya. D., O nekotorykh obschikh zadachakh teorii obyknovennykh differentsialnykh uravnenii i o razlozhenii proizvolnykh funktsii v ryady, Petrograd, 1917

[19] Shamanskii V. E., Metody chislennogo resheniya kraevykh zadach na ETsVM, v. II, Nauk. dumka, Kiev, 1966

[20] Charnyi I. A., Neustanovivsheesya dvizhenie realnoi zhidkosti v trubakh, Nedra, M., 1975

[21] Akhmetzyanov A. V., Salnikov A. M., Spiridonov S. V., “Mnogosetochnye balansovye modeli nestatsionarnykh potokov v slozhnykh gazotransportnykh sistemakh”, Setevye modeli v upravlenii, Upravlenie bolshimi sistemami, 30.1, Spets. vypusk, izd. IPU RAN, M., 2010, 230–251

[22] Aida-zade K. R., Ashrafova E. R., “Raschet neustanovivshikhsya rezhimov techeniya zhidkosti v truboprovodnykh setyakh”, Izv. vtuzov Azerbaidzhana, 2014, no. 1, 60–67