On a Sixth-order Solver for Multiple Roots of Nonlinear Equations

Abstract

A number of iterative schemes with high convergence order to solve nonlinear equations are presented in the literature. In this paper, a sixth-order multiple-zero finder has been developed and the dynamics of selected iterative schemes with uniparametric polynomial weight function are investigated using M\"{o}bius conjugacy map applied to the form $((z-A)(z-B))^m$. The complex dynamics on the Riemann sphere by analyzing the parameter spaces associated with the free critical points are studied and the numerical experiments are carried out.