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：我们提出了求解Volterra积分微分方程的隐式和显式数值算法。这些算法是前期工作的拓展，适用于一般形式的核函数。我们采用合适的测试方程来研究两种算法的稳定性，并通过数值方法推导出稳定区域。隐式方法的稳定区域呈现无界特征，而显式方法的稳定区域为靠近原点的有界区域。我们通过若干数值计算验证了所得结果。