Local convergence and dynamical analysis of a new family of optimal fourth-order iterative methods

Abstract

In this paper, a family of new fourth-order optimal iterative methods for solving nonlinear equations is proposed. The classical King's family of fourth-order schemes is obtained as an special case. We also present results for describing the conjugacy classes and dynamics of some of the presented methods for complex polynomials of different degrees.

Keywords:

• iterative methods
• order of convergence
• rational map
• basin of attraction
• conjugacy classes

2010 AMS Subject Classifications::

• 65H05
• 37N30
• 37F10
• 37D05

Acknowledgement

The authors thank the referees for their valuable comments and for their suggestions to improve the readability of the paper. This research was supported by Ministerio de Ciencia y Tecnología MTM2011-28636-C02-02 and FONDOCYT República Dominicana.