A family of Kurchatov-type methods and its stability

We present a parametric family of iterative methods with memory for solving nonlinear equations, that includes Kurchatov’s scheme, preserving its second-order convergence. By using the tools of multidimensional real dynamics, the stability of members of this family is analyzed on low-degree polynomials, showing that some elements of this class have more stable behavior than the original Kurchatov’s method. We extend this family to multidimensional case and present different numerical tests for several members of the class on nonlinear systems. The numerical results obtained confirm the dynamical analysis made.