Dynamical Analysis via Möbius Conjugacy Map on a Uniparametric Family of Optimal Fourth-Order Multiple-Zero Solvers with Rational Weight Functions

Abstract

A triparametric family of fourth-order multiple-zero solvers have been proposed. In this paper, we select among them a uniparametric family of optimal fourth-order multiple-zero solvers with rational weight functions and pursue their dynamics by exploring the relevant parameter spaces and dynamical planes, by means of Möbius conjugacy map applied to a prototype polynomial of the form (z-A)m(z-B)m. The resulting dynamics is best illustrated through various stability surfaces and parameter spaces as well as dynamical planes.