Solving nonlinear integral equations of Fredholm type with high order iterative methods

The application of high order iterative methods for solving nonlinear integral equations is not usual in mathematics. But, in this paper, we show that high order iterative methods can be used to solve a special case of nonlinear integral equations of Fredholm type and second kind. In particular, those that have the property of the second derivative of the corresponding operator have associated with them a vector of diagonal matrices once a process of discretization has been done.