Two-step Iterative Methods with Sixth-order Convergence for Solving Nonlinear Equations
R. Thukral *
Padé Research Centre, 39 Deanswood Hill, Leeds, West Yorkshire, LS17 5JS, England.
*Author to whom correspondence should be addressed.
Abstract
Two parameter families of sixth-order iterative methods for finding simple zeros of nonlinear equations are developed. The new methods have the order of convergence order of five or six. Per iteration these new methods require two evaluations of the function and two evaluations of the first-order derivatives. In fact, the efficiency index of these methods is 
. Several examples are given to illustrate the efficiency of these new methods and their comparisons with other sixth-order method.
Keywords: Nonlinear equations, order of convergence, computational efficiency, iterative methods