Convergence analysis of Sinc-collocation methods for nonlinear Fredholm integral equations with a weakly singular kernel

In this paper, the efficient methods are proposed for solving nonlinear Fredholm integral equations with a weakly singular kernel. By using Sinc approximation with the single exponential (SE) and double exponential (DE) transformations, the methods are developed. Sinc approximation has considerable advantages. Approximation by Sinc functions handles singularities in the problem and such approximations yield rapidly convergent schemes for solving the problem. Furthermore, convergence of proposed methods is discussed by preparing the theorems which show exponential convergence and guarantee the applicability of those. Finally, some numerical examples are presented to illustrate efficiency and accuracy of the numerical schemes.