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

• Published in: Communications in nonlinear science & numerical simulation 2023-10, Vol.125, p.107398, Article 107398
• Main Authors: Tang, Changyang, Zhang, Chengjian
• Format: Article
• Language: English
• Subjects: Delay boundary feedback; Energy stability; Error analysis; One-parameter spectral Galerkin methods; Timoshenko beam system
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2023.107398

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. •This paper first addresses the numerical methods for Timoshenko beam (TB) system with delay boundary feedback (DBF).•A class of one-parameter spectral Galerkin (OPSG) with parameter θ∈[0,1] are constructed.•Under the given conditions, OPSG methods are proved to have the computational accuracy O(|1−2θ|τ+τ2+N−l).•For external-force-free TB system with DBF, it is shown that OPSG methods can preserve the energy stability.