New Higher Order Iterative Method for Multiple Roots of Nonlinear Equations

In this paper, we propose a new higher order iterative method to find multiple roots of nonlinear equations. The combination of Taylor’s series, Newton’s method and the composition approach are used to derive the new method. It requires three evaluations of the function and two evaluations of the derivative of the function per iteration. The theoretical convergence of the proposed method is proved in the main theorem which establishes sixth order of convergence. We compare the developed method with well-known equivalent existing methods by taking various numerical examples. The numerical results demonstrate the better efficiency of the developed method as compared to some standard iterative methods.