One-parameter spectral Galerkin methods for Timoshenko beam system with delay boundary feedback

Abstract

This paper deals with Timoshenko beam (TB) system with delay boundary feedback (DBF). For external-force-free TB system with DBF, an energy stability criterion is established. For solving general TB system with DBF, a class of one-parameter spectral Galerkin (OPSG) methods with parameter θ∈[0,1] are suggested. It is proved under the appropriate conditions that OPSG methods can preserve the energy stability in the discrete sense. Based on a new projection operator and some analytical techniques, an L2-error estimate of the methods is derived. Finally, by performing several numerical experiments, the obtained theoretical results and the computational accuracy of the methods are further illustrated.