Real Dynamics of a Sixth-Order Family of Derivative-Free Iterative Method Without Memory
摘要
This manuscript introduces the dynamical behavior of a family of sixth-order derivative-free iterative method. When the proposed method is applied on a quadratic equation, and the presence of a parameter \(\mu \in \mathbb {R}\) , the iterative method creates the dynamical plane. Also, the reliability and stability of the iterative method have been studied using different tools. Moreover, information like convergence to n-cycles, different types of fixed points, and the chaotic nature of polynomials are all studied using the convergence plane.