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.