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Iteration Methods with an Auxiliary Function for Nonlinear Equations

Faisal Ali, Waqas Aslam, Imran Khalid, Akbar Nadeem, Antonio Di Crescenzo
2020 Journal of Mathematics  
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
more » ... iewed as the special cases of these methods. We consider the diverse scientific/engineering models to demonstrate the efficiency of the proposed methods.
doi:10.1155/2020/7356408 fatcat:m3hptfgwmjbjzav5ezzs2syg54