Dynamics of subfamilies of Ostrowski-Chun methods

Abstract

Abstract In this paper, we classify the fixed and critical points of the bi-parametric family of Ostrowski–Chun methods applied on quadratic polynomials. We obtain the values of the parameters that reduce the number of free critical points. We select the one-parametric subfamilies with only one free critical point and we carry out a dynamical study of these subfamilies. For each subfamily we study the parameter plane in order to consider which numerical methods are more appropriate for solving nonlinear equations.