In this thesis, a numerical method is proposed for solving nonlinear Fredholm integral equations of the second kind with kernels that may not be differentiable. The main idea consists of approximating the original kernel by a separable kernel obtained via Chebyshev interpolation polynomials. This enables the explicit computation of the inverse of the first Frcehet derivative operator, which is required in Newton's method. By combining this kernel approximation with the Newton--Kantorovich method under Lipschitz conditions, convergence, existence, and uniqueness results for the approximate solution are established. The method is implemented in an infinite-dimensional setting, thereby avoiding full discretization. Furthermore, the proposed approach is compared with the collocation projection method. Finally, numerical examples are provided to evaluate the performance of both the main and the comparative methods.
