A New Class of Fifth and Sixth Order Root-Finding Methods with Its Dynamics and Applications

Authors

  • Debasis Sharma Department of Mathematics, IIIT Bhubaneswar, Odisha 751003, India
  • Sanjaya Kumar Parhi Department of Mathematics, Fakir Mohan University, Odisha 756020, India
  • Shanta Kumari Sunanda Department of Mathematics, IIIT Bhubaneswar, Odisha 751003, India

DOI:

https://doi.org/10.37256/cm.152020606

Keywords:

iterative methods, nonlinear equations, Newton's method, complex dynamics, stability

Abstract

In this paper, we deal with the construction, analysis and applications of a modified uniparametric family of methods to solve nonlinear equations in R. We study the convergence of new methods which shows the order of convergence is at least five and for a particular value 3/2 of the parameter γ, the method is sixth-order convergent. We discuss several applications such as Max Planck’s conservative law, chemical equilibrium, and multi-factor effect to demonstrate the productiveness and capability of the suggested method (for γ = 3/2 ). At every iteration our method is compared with Maroju et al. method[1] and Parhi and Gupta method[2] in terms of the values |f (xn)| and |xnxn−1|. From the numerical experiments, the advantages of our method are observed. Furthermore, we study the complex dynamics to determine the stability and dynamical properties of the methods.

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Published

2020-10-29

How to Cite

1.
Sharma D, Sanjaya Kumar Parhi, Shanta Kumari Sunanda. A New Class of Fifth and Sixth Order Root-Finding Methods with Its Dynamics and Applications. Contemp. Math. [Internet]. 2020 Oct. 29 [cited 2024 Apr. 18];1(5):401-16. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/606