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Iteration Methods with an Auxiliary Function for Nonlinear Equations

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  • Faisal Ali
  • Waqas Aslam
  • Imran Khalid
  • Akbar Nadeem
  • Antonio Di Crescenzo

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.

Suggested Citation

  • Faisal Ali & Waqas Aslam & Imran Khalid & Akbar Nadeem & Antonio Di Crescenzo, 2020. "Iteration Methods with an Auxiliary Function for Nonlinear Equations," Journal of Mathematics, Hindawi, vol. 2020, pages 1-15, October.
    • Handle: RePEc:hin:jjmath:7356408
    DOI: 10.1155/2020/7356408
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    Cited by:

    1. Kamsing Nonlaopon & Awais Gul Khan & Farah Ameen & Muhammad Uzair Awan & Clemente Cesarano, 2022. "Multi-Step Quantum Numerical Techniques for Finding the Solutions of Nonlinear Equations," Mathematics, MDPI, vol. 10(15), pages 1-17, July.

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