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The existence of a solution and a numerical method for the Timoshenko nonlinear wave system
Published online by Cambridge University Press: 15 February 2004
Abstract
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.
- Type
- Research Article
- Information
- ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 1 , January 2004 , pp. 1 - 26
- Copyright
- © EDP Sciences, SMAI, 2004
References
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