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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, advantages of our method is observed. Furthermore, we study the complex dynamics to determine the stability and dynamical properties of the methods.

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