Numerical Approximation and Error Analysis for the Timoshenko Beam Equations with Boundary Feedback

In this paper, the numerical approximation of a Timoshenko beam with boundary feedback is considered. We derived a linearized three-level difference scheme on uniform meshes by the method of reduction of order for a Timoshenko beam with boundary feedback. It is proved that the scheme is uniquely solvable, unconditionally stable and second order convergent in L∞ norm by using the discrete energy method.A numerical example is presented to verify the theoretical results.