Iteration Methods with an Auxiliary Function for Nonlinear Equations

Abstract

Various iterative methods have been introduced by involving Taylor's series on the auxiliary function gx to solve the nonlinear equation fx=0. In this paper, we introduce the expansion of gx with the inclusion of weights wi such that ∑i=1pwi=1 and knots τi∈0,1 in order to develop a new family of iterative methods. The methods proposed in the present paper are applicable for different choices of auxiliary function gx, and some already known methods can be viewed as the special cases of these methods. We consider the diverse scientific/engineering models to demonstrate the efficiency of the proposed methods.