An improvement of the Kurchatov method by means of a parametric modification

In this work, a uniparametric generalization of the iterative method due to Kurchatov is presented. The model presented derivative-free and approximates solution nonlinear equations when operator non-differenciable. As accessibility usually problem in application method, since set initial guesses that guarantee convergence small, main objective work improve its while maintaining even increasing speed convergence. For purpose, we introduce variable parameter function allows us get better approximation derivative by using symmetric uniparameteric first-order divided difference operator. We perform complex dynamic study corroborate improvements region. Moreover, complete analysis local semilocal established for new method. Finally, apply theoretical results solve integral equation showing usefulness work.