Geodesic
The existence of a solution and a numerical method for the Timoshenko nonlinear wave system
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 1, pp. 1-26

Voir la notice de l'article provenant de la source Numdam

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.

DOI : 10.1051/m2an:2004001
Classification : 35Q, 65M
Keywords: 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 },
     pages = {1--26},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {1},
     year = {2004},
     doi = {10.1051/m2an:2004001},
     mrnumber = {2073928},
     zbl = {1080.35159},
     language = {en},
     url = {http://geodesic.mathdoc.fr/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 
PY  - 2004
SP  - 1
EP  - 26
VL  - 38
IS  - 1
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004001/
DO  - 10.1051/m2an:2004001
LA  - en
ID  - M2AN_2004__38_1_1_0
ER  - 
%0 Journal Article
%A Peradze, Jemal
%T The existence of a solution and a numerical method for the Timoshenko nonlinear wave system
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2004
%P 1-26
%V 38
%N 1
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004001/
%R 10.1051/m2an:2004001
%G en
%F M2AN_2004__38_1_1_0
Peradze, Jemal. The existence of a solution and a numerical method for the Timoshenko nonlinear wave system. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 1, pp. 1-26. doi: 10.1051/m2an:2004001

Cité par Sources :