In this study, the second kind Volterra integral equations (VIEs) are considered. An algorithm based on the two-point Taylor formula as a special case of the Hermite interpolation is proposed to approximate the solution of such problems. The method can be applied for solving both the linear and nonlinear VIEs and systems of nonlinear VIEs. The convergence analysis and the error estimate of the method are described. A multistep form of the algorithm which is particularly beneficial in large intervals is also presented. The main advantage of the proposed algorithm is that it gives high accurate results in acceptable computational times. In order to indicate the validity of the method, it is employed for solving several illustrative examples. The efficiency of the method is confirmed through our study respecting the absolute errors and CPU times.

在这项研究中，考虑了第二类Volterra积分方程（VIE）。提出了一种基于两点泰勒公式作为Hermite插值特例的算法，以近似求解此类问题。该方法可用于求解线性和非线性VIE以及非线性VIE的系统。描述了该方法的收敛性分析和误差估计。还提出了算法的多步形式，该形式在大间隔中特别有用。所提出算法的主要优点是，它可以在可接受的计算时间内给出高精度的结果。为了表明该方法的有效性，将其用于解决几个说明性示例。通过我们的研究，确认了该方法的效率，同时考虑了绝对误差和CPU时间。