Dynamical analysis via Möbius conjugacy map on a uniparametric family of optimal fourth-order multiple-zero solvers with rational weight functions (Q1727233)

Summary: 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.