Geodesic
Difference approximation of the problem of bending vibrations of a thin elastic plate
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 4, pp. 718-740 
A. A. Kuleshov. Difference approximation of the problem of bending vibrations of a thin elastic plate. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 4, pp. 718-740. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_4_a13/
@article{ZVMMF_2005_45_4_a13,
     author = {A. A. Kuleshov},
     title = {Difference approximation of the problem of bending vibrations of a thin elastic plate},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {718--740},
     year = {2005},
     volume = {45},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_4_a13/}
}
TY  - JOUR
AU  - A. A. Kuleshov
TI  - Difference approximation of the problem of bending vibrations of a thin elastic plate
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2005
SP  - 718
EP  - 740
VL  - 45
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_4_a13/
LA  - ru
ID  - ZVMMF_2005_45_4_a13
ER  - 
%0 Journal Article
%A A. A. Kuleshov
%T Difference approximation of the problem of bending vibrations of a thin elastic plate
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2005
%P 718-740
%V 45
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_4_a13/
%G ru
%F ZVMMF_2005_45_4_a13

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

The problem of bending vibrations of a thin elastic plate is considered. A difference method is proposed for solving the problem. The convergence of the solution of the difference problem to a generalized solution of the original differential problem is proved and the rate of convergence is estimated.

[1] Timoshenko S. P., Voinovskii-Kriger S., Plastinki i obolochki, Fizmatgiz, M., 1963

[2] Babakov I. M., Teoriya kolebanii, Nauka, M., 1968 | MR

[3] Landau L. D., Livshits E. M., Teoriya uprugosti, Nauka, M., 1987 | MR | Zbl

[4] Ogibalov P. M., Izgib, ustoichivost i kolebaniya plastinok, Izd-vo MGU, M., 1958

[5] Samarskii A. A., Gulin A. V., Ustoichivost raznostnykh skhem, Nauka, M., 1973 | Zbl

[6] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1977 | MR | Zbl

[7] Marchuk G. I., Metody vychislitelnoi matematiki, Nauka, M., 1980 | MR

[8] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973 | MR

[9] Osipov Yu. S., Vasilev F. P., Potapov M. M., Osnovy metoda dinamicheskoi regulyarizatsii, Izd-vo MGU, M., 1999

[10] Zlotnik A. A., “Otsenka skorosti skhodimosti proektsionno-setochnykh metodov dlya giperbolicheskikh uravnenii vtorogo poryadka”, Vychisl. protsessy i sistemy, 8, Nauka, M., 1991, 116–167 | MR

[11] Lions J. L., Magenes E., Non homogeneous boundary value problems and applications, v. 2, Springer, Berlin ets., 1972

[12] Kuleshov A. A., “Raznostnaya approksimatsiya i regulyarizatsiya odnoi zadachi optimalnogo upravleniya protsessom, opisyvaemym ellipticheskim uravneniem”, Dokl. AN SSSR, 269:4 (1983), 809–813 | MR | Zbl

[13] Samarskii A. A., Lazarov R. D., Makarov V. L., Raznostnye skhemy dlya differentsialnykh uravnenii s obobschennymi resheniyami, Vyssh. shkola, M., 1987