The initial boundary value problem for a beam is considered in the Timoshenko model. Assuming the analyticity of the initial conditions, it is proved that the problem is solvable throughout the time interval. After that, a numerical algorithm, consisting of three steps, is constructed. The solution is approximated with respect to the spatial and time variables using the Galerkin method and a Crank-Nicholson type scheme. The system of equations obtained by discretization is solved by a version of the Picard iteration method. The accuracy of the proposed algorithm is investigated.
Classification : 35Q, 65M
Mots clés : Timoshenko nonlinear system, beam, Galerkin method, Crank-Nicholson scheme, Picard process
@article{M2AN_2004__38_1_1_0,
author = {Peradze, Jemal},
title = {The existence of a solution and a numerical method for the {Timoshenko} nonlinear wave system},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
pages = {1--26},
publisher = {EDP-Sciences},
volume = {38},
number = {1},
year = {2004},
doi = {10.1051/m2an:2004001},
zbl = {1080.35159},
mrnumber = {2073928},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2004001/}
}
TY - JOUR AU - Peradze, Jemal TI - The existence of a solution and a numerical method for the Timoshenko nonlinear wave system JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique PY - 2004 DA - 2004/// SP - 1 EP - 26 VL - 38 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2004001/ UR - https://zbmath.org/?q=an%3A1080.35159 UR - https://www.ams.org/mathscinet-getitem?mr=2073928 UR - https://doi.org/10.1051/m2an:2004001 DO - 10.1051/m2an:2004001 LA - en ID - M2AN_2004__38_1_1_0 ER -
Peradze, Jemal. The existence of a solution and a numerical method for the Timoshenko nonlinear wave system. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 38 (2004) no. 1, pp. 1-26. doi : 10.1051/m2an:2004001. http://www.numdam.org/articles/10.1051/m2an:2004001/
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