In this paper, we study a class of block collocation boundary value methods for the first-kind Volterra integral equations. The numerical algorithm is constructed by utilizing approximations to the exact solution in future steps. The solvability of the new method is not ensured, even for the uniform mesh. Therefore, we discuss its solvability by studying the special structure of the collocation equation and present the sufficient condition for the existence of the collocation solution. Furthermore, we exploit the convergence property with the help of interpolation remainders. Finally, numerical experiments are conducted to show the effectiveness of the new boundary value method and verify given theoretical results.

在本文中，我们研究了第一类Volterra积分方程的一类块配置边值方法。通过在将来的步骤中利用对精确解的近似来构造数值算法。即使对于均匀的网格，也无法确保新方法的可溶解性。因此，我们通过研究搭配方程的特殊结构来讨论其可解性，并为搭配解的存在提供了充分的条件。此外，我们借助内插余数来利用收敛性。最后，通过数值实验证明了新边界值方法的有效性，并验证了给出的理论结果。