A numerical algorithm for the nonlinear Timoshenko beam system.

An initial boundary value problem is considered for the dynamic beam system wtt=cd−a+b∫01wx2dxwxx−cdψx,ψtt=cψxx−c2d(ψ−wx). Its solution is found by means of an algorithm, the constituent parts of which are the finite element method, the implicit symmetric difference scheme used to approximate the solution with respect to the spatial and time variables, and also a Picard type iteration process for solving the system of nonlinear equations obtained by discretization. Errors of three parts of the algorithm are estimated and, as a result, its total error estimate is obtained. A numerical example is solved. [ABSTRACT FROM AUTHOR]