Family of optimal two-step fourth order iterative method and its extension for solving nonlinear equations

Abstract

In this paper, the weight function technique is utilized to develop new family of two-step fourth order convergence iterative methods for approximating the solution of nonlinear equations. The methods require the evaluation of three distinct functions evaluation per iteration circle and as such, are optimal in agreement with the Kung-Traub’s conjecture. This developed family of methods is further extended to design another new family of four-step ninth order convergence with efficiency index EI = 1.5518. We carried out the convergence analysis of the two families of iterative methods. This analysis provided us with information about the flexibility of the weight function in the method used in constructing other new families of iterative methods. The methods are applied to solve some nonlinear equations and real life problems that are modeled into nonlinear equations. The results obtained from computation experience are compared with some of its existing contemporary methods.

Subject Classification: (2010):

• Primary 65H05
• Secondary 65Hxx

Keywords:

• Nonlinear equation
• Iterative method
• Weight function
• Kung-Traub conjecture