Family of Optimal Fourth Order Methods for Multiple Roots and their Dynamics

Abstract

In this paper, we propose a family of fourth order method for solving non-linear equations with multiple roots. The method is based on the arithmetic mean of Weerakoon method and Chebyshev method for multiple roots. Some numerical examples are provided in support of the theoretical results. The numerical results obtained by the method for different values of the parameter are compared with some known methods. The dynamical behaviour of methods is discussed and basins of attraction around the multiple roots for some polynomial is shown at the end of the work.