A sinc quadrature method for the Urysohn integral equation

Abstract

In this paper, we study the numerical approximation of the Urysohn integral equation with two methods. The methods are developed by means of the sinc approximation with the Single Exponential (SE) and Double Exponential (DE) transformations. These numerical methods combine a sinc Nystr\"{o}m method with the {N}ewton iterative process that involves solving a nonlinear system of equations. We provide an error analysis for the methods. These methods improve conventional results and achieve exponential convergence. Some numerical examples are given to confirm the accuracy and ease of implementation of the methods.