Two different Sinc-collocation methods for Volterra integral equations of the second kind have been independently proposed by Stenger and Rashidinia--Zarebnia. However, their relationship remains unexplored. This study theoretically examines the solutions of these two methods, and reveals that they are not generally equivalent, despite coinciding at the collocation points. Strictly speaking, Stenger's method assumes that the kernel of the integral is a function of a single variable, but this study theoretically justifies the use of his method in general cases, i.e., the kernel is a function of two variables. Then, this study rigorously proves that both methods can attain the same, root-exponential convergence. In addition to the contribution, this study improves Stenger's method to attain significantly higher, almost exponential convergence. Numerical examples supporting the theoretical results are also provided.

翻译：Stenger与Rashidinia--Zarebnia分别独立提出了两种不同的求解第二类Volterra积分方程的Sinc配置法。然而，这两种方法之间的关系尚未得到探究。本研究从理论上检验了这两种方法的解，并揭示出尽管在配置点处重合，但它们在一般情况下并不等价。严格来说，Stenger方法假设积分核是单变量函数，但本研究从理论上论证了该方法在一般情况下的适用性，即积分核为双变量函数的情形。随后，本研究严格证明了两种方法均可达到相同的根指数收敛阶。除上述贡献外，本研究还改进了Stenger方法，使其获得显著更高的、近乎指数级的收敛速度。文中亦提供了支持理论结果的数值算例。