A FOURTH ORDER ENERGY STABLE FINITE DIFFERENCE SCHEME FOR A TIMOSHENKO BEAM EQUATIONS WITH LOCALLY DISTRIBUTED FEEDBACK

Abstract

This work deals with the numerical solution of a control problem governed by the Timoshenko beam equations with locally distributed feedback. We apply a fourth-order Compact Finite Difference (CFD) approximation for the discretizing spatial derivatives and a Forward second order method for the resulting linear system of ordinary differential equations. Using the energy method, we derive energy relation for the continuous model, and design numerical scheme that preserve a discrete analogue of the energy relation. Numerical results show that the CFD approximation of fourth order give an efficient method for solving the Timoshenko beam equations.