We describe an algorithm, based on Euler's method, for solving Volterra integro-differential equations. The algorithm approximates the relevant integral by means of the composite Trapezium Rule, using the discrete nodes of the independent variable as the required nodes for the integration variable. We have developed an error control device, using Richardson extrapolation, and we have achieved accuracy better than 1e-12 for all numerical examples considered.

翻译：本文描述了一种基于欧拉方法的算法，用于求解Volterra积分-微分方程。该算法通过复合梯形法则逼近相关积分，利用自变量的离散节点作为积分变量所需的节点。我们采用Richardson外推法开发了一种误差控制机制，并在所有数值算例中实现了优于1e-12的计算精度。