In this study, main concern is focused on numerically solving the integro-differential-delay equations with variable coefficients and infinite boundary on half-line, proposing a matrix-collocation method based on the orthoexponential polynomials. The method is equipped with the collocation points and the hybridized matrix relations between the orthoexponential and Taylor polynomials, which enable us to convert an integral form with infinite boundary into a mathematical formulation. The method also directly establishes the verification of the existence and uniqueness of this integral form through a convergent result. In order to observe the validity of the method versus its computation limit, an error bound analysis is performed by using the upper bound of the orthoexponential polynomials. A computer module containing main infrastructure of the method is specifically designed and run for providing highly precise results. Thus, the numerical and graphical implementations are completely monitored in table and figures, respectively. Based on the comparisons and findings, one can state that the method is remarkable, dependable, and accurate for approaching the aforementioned equations.

在这项研究中，主要关注点集中在数值求解半线上具有可变系数和无限边界的积分-微分-延迟方程，提出了一种基于正交指数多项式的矩阵配置方法。该方法具有配置点和正交指数与泰勒多项式之间的混合矩阵关系，这使我们能够将具有无限边界的积分形式转换为数学公式。该方法还通过收敛的结果直接建立对该积分形式的存在性和唯一性的验证。为了观察该方法相对于其计算极限的有效性，通过使用正交指数多项式的上限执行误差界限分析。专门设计并运行了包含该方法主要基础结构的计算机模块，以提供高度精确的结果。因此，分别在表和图中完全监视数字和图形实现。根据比较和发现，可以说该方法对于逼近上述方程式是显着，可靠和准确的。