Some improvements of Jarratt’s method with sixth-order convergence

摘要

In this paper, we present a one-parameter family of variants of Jarratt’s fourth-order method for solving nonlinear equations. It is shown that the order of convergence of each family member is improved from four to six even though it adds one evaluation of the function at the point iterated by Jarratt’s method per iteration. Several numerical examples are given to illustrate the performance of the presented methods.