Accelerated iterative methods for finding solutions of nonlinear equations and their dynamical behavior
In this paper, we present a family of optimal, in the sense of KungTraubs conjecture, iterative methods for solving nonlinear equations with eighth-order convergence. Our methods are based on Chuns fourth-order method. We use the Ostrowskis efficiency index and several numerical tests in order to compare the new methods with other known eighth-order ones. We also extend this comparison to the dynamical study of the different methods.
iterative methods nonlinear equations efficiency index convergence order basin of attraction periodic orbit dynamical plane 65b99 65h05 65p99 37f10