Dynamical Analysis on a Family of Sixth-order Multiple-zero Solver with Polynomial and Rational Weight Functions (European Journal of Pure and Applied Mathematics, 2026)
A sixth-order family of three-point multiple root solvers with polynomial and rational weight functions are investigated by means of Möbius conjugacy map applied to a prototype polynomial of the form $ (z-p)^m (z-q)^m $ with the related parameter spaces and dynamical planes. The interesting dynamics is shown through various stability surfaces and parameter spaces including dynamical planes.
Keywords: conjugacy map, multiple root, nonlinear equation, parameter space