Sinc-collocation methods for Volterra-Fredholm integral equations of the second kind were proposed in 2012 and 2013 by multiple authors independently. Their theoretical analyses and numerical experiments suggest that the presented methods can attain root-exponential convergence. However, convergence of those methods was not strictly proved. This study first improves their methods to be easy to implement, and provides a convergence theorem of the improved method. For the same equations, another Sinc-collocation method was proposed in 2016. The method is regarded as improvement of the variable transformation in the method proposed in 2012. The method in 2016 may attain a higher rate than that of the previous methods, but its convergence was not strictly proved. For the method in 2016 as well, this study improves it to be easy to implement, and provides a convergence theorem.

翻译：针对第二类Volterra-Fredholm积分方程的Sinc配置法于2012年和2013年由多位学者独立提出。其理论分析与数值实验表明，所提方法可获得根指数阶收敛。然而，这些方法的收敛性并未得到严格证明。本研究首先改进了原方法以提升其易实施性，并给出了改进方法的收敛定理。针对同一类方程，2016年提出了另一种Sinc配置法。该方法被视为对2012年所提方法中变量变换的改进。2016年的方法可能获得比先前方法更高的收敛速率，但其收敛性同样未获严格证明。针对2016年的方法，本研究同样进行了易实施性改进，并给出了相应的收敛定理。