Abstract
We consider in this article a nonlinear vibrating Timoshenko system with thermoelasticity with second sound. We first recall the results obtained in [ 2 ] concerning the well-posedness, the regularity of the solutions and the asymptotic behavior of the associated energy. Then, we use a fourth-order finite difference scheme to compute the numerical solutions and we prove its convergence. The energy decay in several cases, depending on the stability number \begin{document}$ \mu $\end{document} , are numerically and theoretically studied.
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