Iteration Methods with an Auxiliary Function for Nonlinear Equations. (27th October 2020) - Ali, Faisal
Abstract : Various iterative methods have been introduced by involving Taylor's series on the auxiliary function g x to solve the nonlinear equation f x = 0 . In this paper, we introduce the expansion of g x with the inclusion of weights w i such that ∑ i = 1 p w i = 1 and knots τ i ∈ 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 g x, 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.