In this paper, we introduce a numerical method to obtain an accurate approximate solution of the integro-differential delay equations with state-dependent bounds. The method is based basically on the generalized Mott polynomial with the parameter-\(\beta\), Chebyshev–Lobatto collocation points and matrix structures. These matrices are gathered under a unique matrix equation and then solved algebraically, which produce the desired solution. We discuss the behavior of the solutions, controlling their parameterized form via \(\beta\) and so we monitor the effectiveness of the method. We improve the obtained solutions by employing the Mott-residual error estimation. In addition to comparing the results in tables, we also illustrate the solutions in figures, which are made up of the phase plane, logarithmic and standard scales. All results indicate that the present method is simple-structured, reliable and straightforward to write a computer program module on any mathematical software.

中文翻译：

---

带有状态依赖的积分微分时滞方程的控制参数数值方法，通过广义Mott多项式

在本文中，我们引入了一种数值方法来获得具有状态依赖范围的积分微分延迟方程的精确近似解。该方法基本上基于具有参数\\（\ beta \），Chebyshev–Lobatto搭配点和矩阵结构的广义Mott多项式。这些矩阵在唯一的矩阵方程式下收集，然后进行代数求解，从而产生所需的解。我们讨论解决方案的行为，通过\（\ beta \）控制其参数化形式因此，我们监控了该方法的有效性。我们通过采用Mott残差估计来改进获得的解决方案。除了比较表中的结果外，我们还用数字说明解决方案，这些解决方案由相平面，对数和标准比例组成。所有结果表明，本方法结构简单，可靠，简单，可以在任何数学软件上编写计算机程序模块。