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 $ \mu $, are numerically and theoretically studied.

中文翻译：

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具有第二声热弹性的铁木辛哥型系统的数值解

我们在本文中考虑了具有第二声音热弹性的非线性振动 Timoshenko 系统。我们首先回忆一下[2] 关于适定性、解的规律性和相关能量的渐近行为。然后，我们使用四阶有限差分格式来计算数值解并证明其收敛性。几种情况下的能量衰减取决于稳定数 $ \mu $，进行了数值和理论研究。