The Dynamical Analysis of a Biparametric Family of Six-Order Ostrowski-Type Method under the Möbius Conjugacy Map

Abstract

In this paper, a family of Ostrowski-type iterative schemes with a biparameter was analyzed. We present the dynamic view of the proposed method and study various conjugation properties. The stability of the strange fixed points for special parameter values is studied. The parameter spaces related to the critical points and dynamic planes are used to visualize their dynamic properties. Eventually, we find the most stable member of the biparametric family of six-order Ostrowski-type methods. Some test equations are examined for supporting the theoretical results.

Keywords

• Möbius conjugacy
• strange fixed points
• stability
• free critical points
• parameter space
• dynamic plane