Improvement of Sinc-collocation methods for Volterra-Fredholm integral equations of the second kind and their theoretical analysis

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.