Local convergence and the dynamics of a family of high convergence order method for solving nonlinear equations

Abstract

We present the local convergence analysis and the study of the dynamics of a higher order iterative method in order to approximate a locally unique solution of multiplicity greater than one of a nonlinear equation. The convergence is obtained by means of using a center-Hölder condition in which the ball of convergence is greater than in previous studies. Moreover, the dynamics of the method are also presented. Numerical examples validating the theoretical results are also provided.