| Issue |
ESAIM: M2AN
Volume 38, Number 1, January-February 2004
|
|
|---|---|---|
| Page(s) | 1 - 26 | |
| DOI | https://doi.org/10.1051/m2an:2004001 | |
| Published online | 15 February 2004 | |
The existence of a solution and a numerical method for the Timoshenko nonlinear wave system
Department of Applied Mathematics and Computer Sciences
of Tbilisi State University,
Tbilisi, 380043, R. of Georgia. j_peradze@yahoo.com.
Received:
24
July
2003
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.
Mathematics Subject Classification: 35Q / 65M
Key words: Timoshenko nonlinear system / beam / Galerkin method / Crank–Nicholson scheme / Picard process.
© EDP Sciences, SMAI, 2004
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.