efficient quadrature methods for solving hammerstein integral equations on the half-line

In this paper, we proposed two numerical methods to solve the nonlinear integral equations of hammerstein type on the half-line. by using a sinc-nyström method based on single-exponential (se) and double-exponential (de) transformations, the problem is converted into a nonlinear system of equations. we provided an error analysis of the proposed schemes and showed that these methods have exponential convergence rates. finally, several numerical examples are given to show the effectiveness of the methods.