An Optimal Fourth-Order Iterative Method for Multiple Roots of Nonlinear Equations

In this paper, we are presenting an iterative scheme for solving nonlinear equations having multiple roots. The newly developed scheme is an improvement of a method for simple roots and it satisfy the Kung-Traub conjecture, so it is optimal. The weight functional approaches used to develop the method. We have analysed its convergence order and proved it. The methods are numerically compared with known methods in terms of the convergence behaviour of convergence, it shows that the developed schemes are superior to existing methods.