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, p. 1-26
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.
@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},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {1},
     year = {2004},
     pages = {1-26},
     doi = {10.1051/m2an:2004001},
     zbl = {1080.35159},
     mrnumber = {2073928},
     language = {en},
     url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Tome 38 (2004) no. 1, pp. 1-26. doi : 10.1051/m2an:2004001. http://www.numdam.org/item/M2AN_2004__38_1_1_0/

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