We present implicit and explicit versions of a numerical algorithm for solving a Volterra integro-differential equation. These algorithms are an extension of our previous work, and cater for a kernel of general form. We use an appropriate test equation to study the stability of both algorithms,, numerically deriving stability regions. The region for the implicit method appears to be unbounded, while the explicit has a bounded region close to the origin. We perform a few calculations to demonstrate our results.

翻译：我们提出求解Volterra积分微分方程的隐式与显式数值算法。这两种算法是我们先前工作的扩展，适用于一般形式的核函数。通过选取合适的测试方程，我们研究了两种算法的稳定性，并数值推导出稳定区域。隐式方法的稳定区域呈现无界特性，而显式方法的稳定区域则局限于原点附近的有界区域。为验证结论，我们进行了若干数值计算。