Iteration Methods with an Auxiliary Function for Nonlinear Equations. (27th October 2020)

• Record Type: Journal Article
• Authors: Ali, Faisal; Aslam, Waqas; Khalid, Imran; Nadeem, Akbar
• Other Names: Di Crescenzo Antonio Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2020(2020)
• Publication Date: 2020-10-27
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2020/7356408
• Languages: English
• ISSNs: 2314-4629

Abstract

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.