Toward efficient numerical solutions of non-linear integral equations with TLD algorithm

This study focuses on a specific type of non-linear second-order integral equations defined over a considerable interval. We propose a new numerical method, the TLD, in three phases: transformation of the equation, linearization via the Newton-Kantorovich method, and discretization with the Nyström technique. We theoretically define the convergence conditions and illustrate the accuracy of our method on several practical examples.