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

Abstract

Sinc-collocation methods for Volterra-Fredholm integral equations of the second kind were proposed independently by multiple authors: by Shamloo et al. in 2012 and by Mesgarani and Mollapourasl in 2013. Their theoretical analyses and numerical experiments suggest that the presented methods can attain root-exponential convergence. However, their convergence has not been strictly proved. This study improves these methods to facilitate implementation, and provides a convergence theorem for the improved method. For the same equations, another Sinc-collocation method was proposed in 2016 by John and Ogbonna, which is regarded as an improvement to the variable transformation employed by Shamloo et al. It may attain a higher rate than the previous methods, but its convergence has not yet been proved. Therefore, this study improves it to facilitate implementation, and provides a convergence theorem for the improved method.