Optimal iterative methods for finding multiple roots of nonlinear equations using weight functions and dynamics

Abstract

[EN] In this paper, we propose a family of iterative methods for finding multiple roots, with known multiplicity, by means of the introduction of four univariate weight functions. With the help of these weight functions, that play an important role in the development of higher order convergent iterative techniques, we are able to construct three-point eight-order optimal multiple-root finders. Also, numerical experiments have been applied to a number of test equations for different special schemes from this family satisfying the conditions given in the convergence analysis. We have also compared the basins of attraction of some proposed and known methods in order to check the wideness of the sets of converging initial points for each problem. (C) 2018 Elsevier B.V. All rights reserved.