A New Class of Fifth and Sixth Order Root-Finding Methods with Its Dynamics and Applications
Author:
Sharma Debasis,Sanjaya Kumar Parhi ,Shanta Kumari Sunanda
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 |xn − xn−1|. From the numerical experiments, advantages of our method is observed. Furthermore, we study the complex dynamics to determine the stability and dynamical properties of the methods.
Publisher
Universal Wiser Publisher Pte. Ltd