Research article

New higher order iterative methods for solving nonlinear equations and their basins of attraction

Abstract

In this work, we have developed a family of eighth order Newton-type methods for solving nonlinear equations with four functional evaluations. Further, we have improved a new member of eighth ordermethod to sixteenth order iterative method with five function evaluations. These two methods are satisfying Kung-Traub Conjecture and their efficiency indices are 1.682 and 1.741. Numerical results are carried out to validate the new methods and some existing compared methods. We consider a concrete variety of real life problems such as projectile motion, Planck’s radiation law, the trajectory of electron in air gap two parallel plates between, Van der Waal’s equation which explains the behavior of a real gas by introducing in the ideal gas equations, in order to check the applicability and effectiveness of our proposed methods. Finally, the basins of attraction are also given to demonstrate their dynamical behavior in the complex plane.