Numerical solutions for a Timoshenko-type system with thermoelasticity with second sound

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