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

Fule Li 1*, Kaimei Huang 1

1 School of Science, Laiyang Agricultural College, Qingdao 266109, China

Received April 27, 2006; Accepted (in revised version) July 7, 2006

Abstract

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

Correspondence to: Fule Li , School of Science, Laiyang Agricultural College, Qingdao 266109, China Email: lfl2004666@126.com