A New Class of Fifth and Sixth Order Root-Finding Methods with Its Dynamics and Applications
Keywords:iterative methods, nonlinear equations, Newton's method, complex dynamics, stability
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 and Parhi and Gupta method in terms of the values |f (xn)| and |xn − xn−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.