Linearization-Discretization process to solve systems of nonlinear Fredholm integral equations in an infinite-dimensional context

In this paper, we propose a different way for solving systems of nonlinear Fredholm integral equations the second kind. We construct our new strategy in two steps, through beginning with linearization phase system by applying Newton method, then pass to discretization some involved operator using Nystr\"{o}m method. The convergence analysis method is proved under necessary conditions. At last, numerical application approach integro-differential equation process taken confirm its advantage.