@article{ZVMMF_2003_43_11_a7,
author = {D. B. Volkov-Bogorodskii and A. N. Danilin and E. B. Kuznetsov and V. I. Shalashilin},
title = {Implicit methods for integration of initial value problems for parameterized systems of second-order ordinary differential equations},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1684--1696},
year = {2003},
volume = {43},
number = {11},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_11_a7/}
}
TY - JOUR AU - D. B. Volkov-Bogorodskii AU - A. N. Danilin AU - E. B. Kuznetsov AU - V. I. Shalashilin TI - Implicit methods for integration of initial value problems for parameterized systems of second-order ordinary differential equations JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2003 SP - 1684 EP - 1696 VL - 43 IS - 11 UR - http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_11_a7/ LA - ru ID - ZVMMF_2003_43_11_a7 ER -
%0 Journal Article %A D. B. Volkov-Bogorodskii %A A. N. Danilin %A E. B. Kuznetsov %A V. I. Shalashilin %T Implicit methods for integration of initial value problems for parameterized systems of second-order ordinary differential equations %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2003 %P 1684-1696 %V 43 %N 11 %U http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_11_a7/ %G ru %F ZVMMF_2003_43_11_a7
D. B. Volkov-Bogorodskii; A. N. Danilin; E. B. Kuznetsov; V. I. Shalashilin. Implicit methods for integration of initial value problems for parameterized systems of second-order ordinary differential equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 43 (2003) no. 11, pp. 1684-1696. http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_11_a7/
[1] Lure A. I., Analiticheskaya mekhanika, Fizmatgiz, M., 1961 | MR
[2] Bathe K.-J., Wilson E. L., Numerical methods in finite element analysis, Prentice-Hall, Inc., Englewood Cliffs, New Jersy, 1976 | Zbl
[3] Danilin A. N., “Nelineinye uravneniya dvizheniya gibkikh sterzhnevykh sistem”, Izv. RAN. Mekhan. tverdogo tela, 1994, no. 1, 177–188
[4] Danilin A. N., “Ploskaya zadacha dinamiki kosmicheskikh sistem s gibkimi odnomernymi elementami”, Vestn. MAI, 2:1 (1995), 61–68
[5] Shklyarchuk F. N., “Nelineinye i linearizovannye uravneniya dvizheniya uprugikh kosmicheskikh konstruktsii”, Izv. RAN. Mekhan. tverdogo tela, 1996, no. 1, 161–175
[6] Danilin A. N., Grishanina T. V., Shklyarchuk F. N., Buzlaev D. V., “Dynamics of a space vehicle with elastic deploying tether”, Comput. and Structures, 72 (1999), 141–147 | DOI | Zbl
[7] Pontryagin L. S., Obyknovennye differentsialnye uravneniya, Nauka, M., 1982 | MR | Zbl
[8] Arnold V. I., Obyknovennye differentsialnye uravneniya, Nauka, M., 1984 | MR
[9] Grigolyuk E. I., Shalashilin V. I., Problemy nelineinogo deformirovaniya, Nauka, M., 1988 | MR | Zbl
[10] Shalashilin V. I., Kuznetsov E. B., “Zadacha Koshi dlya nelineino deformiruemykh sistem kak zadacha prodolzheniya resheniya po parametru”, Dokl. RAN, 329:4 (1993), 426–428 | MR | Zbl
[11] Kuznetsov E. B., Shalashilin V. I., “Zadacha Koshi kak zadacha prodolzheniya resheniya po parametru”, Zh. vychisl. matem. i matem. fiz., 33:12 (1993), 1792–1805 | MR | Zbl
[12] Shalashilin V. I., Kuznetsov E. B., “Nailuchshii parametr prodolzheniya resheniya”, Dokl. RAN, 334:5 (1994), 566–568 | MR | Zbl
[13] Kuznetsov E. B., Shalashilin V. I., “Zadacha Koshi dlya mekhanicheskikh sistem s konechnym chislom stepenei svobody kak zadacha prodolzheniya po nailuchshemu parametru”, Prikl. matem. i mekhan., 58:6 (1994), 14–21 | MR
[14] Shalashilin V. I., Kuznetsov E. B., Metod prodolzheniya resheniya po parametru i nailuchshaya parametrizatsiya, Editorial URSS, M., 1999 | MR
[15] Danilin A. N., Shalashilin V. I., “O parametrizatsii nelineinykh uravnenii deformirovaniya tverdogo tela”, Izv. RAN. Mekhan. tverdogo tela, 2000, no. 1, 82–92
[16] Khairer E., Nersett S., Vanner G., Reshenie obyknovennykh differentsialnykh uravnenii. Nezhestkie zadachi, Mir, M., 1990 | MR
[17] Khairer E., Vanner G., Reshenie obyknovennykh differentsialnykh uravnenii. Zhestkie i differentsialno-algebraicheskie zadachi, Mir, M., 1999
[18] Bakhvalov N. S., Chislennye metody, Nauka, M., 1973 | MR | Zbl
[19] Danilin A. N., Kuznetsov E. B., Shalashilin V. I., “The best parametrization and numerical solution of the Cauchy problem for a system of ordinary differential equations of the second order”, Funct. Different. Equations, 8:1–2 (2001), 141–146 | MR | Zbl
[20] Danilin A. N., Volkov-Bogorodskii D. B., “O neyavnykh metodakh integrirovaniya parametrizovannykh uravnenii nelineinykh dinamicheskikh sistem”, Vestn. MAI, 8:2 (2001), 40–52 | MR
[21] Kopylov A. V., Kuznetsov E. B., “Ob odnom podkhode k chislennomu integrirovaniyu zadachi Koshi dlya differentsialnykh uravnenii s zapazdyvaniem”, Zh. vychisl. matem. i matem. fiz., 41:10 (2001), 1547–1556 | MR | Zbl