The main purpose of this work is to provide a numerical approach for linear second-order differential and integro-differential equations with constant delay. An algorithm based on the use of Taylor polynomials is developed to construct a collocation solution [Formula: see text] for approximating the solution of second-order linear DDEs and DIDEs. It is shown that this algorithm is convergent. Some numerical examples are included to demonstrate the validity of this algorithm.

中文翻译：

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泰勒搭配法求解二阶线性时滞微分和积分微分方程

这项工作的主要目的是为具有恒定延迟的线性二阶微分和积分微分方程提供一种数值方法。开发了一种基于使用泰勒多项式的算法来构造一个搭配解[公式：见正文]，用于逼近二阶线性 DDE 和 DIDE 的解。证明该算法是收敛的。包括一些数值例子来证明该算法的有效性。