Fule Li ^1*, Kaimei Huang ¹

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 $L_{\infty}$ norm by using the discrete energy method. A numerical example is presented to verify the theoretical results.

Key words: Timoshenko beam; boundary feedback; partial differential equation; finite difference; solvability; convergence; stability.

AMS subject classifications: 65M06, 65M12, 65M15