  In this paper, two numerical schemes for a nonlinear integral equation of
Fredholm type with weakly singular kernel are proposed. These numerical methods
combine sinc-collocation and sinc-convolution approximations with Newton and
steepest descent iterative methods that involve solving a nonlinear system of
equations. The convergence rate of the approximation schemes is also analyzed.
Numerical experiments have been performed to illustrate the sharpness of the
theoretical estimates and the sensitivity of the solution with respect to some
parameters in the equation. The comparison between the schemes indicates that
sinc-convolution method is more effective.
