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. firstname.lastname@example.org.
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