Toward Efficient Numerical Solutions of Nonlinear Integral Equations with (T.L.D) Algorithm

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