Behind Jarratt’s Steps: Is Jarratt’s Scheme the Best Version of Itself?

Abstract

In this paper, we analyze the stability of the family of iterative methods designed by Jarratt using complex dynamics tools. This allows us to conclude whether the scheme known as Jarratt’s method is the most stable among all the elements of the family. We deduce that classical Jarratt’s scheme is not the only stable element of the family. We also obtain information about the members of the class with chaotical behavior. Some numerical results are presented for confirming the convergence and stability results.