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Fractal Behavior of King’s Optimal Eight-Order Iterative Method and Its Numerical Application

Wenshuo Li orcid.org/0000-0001-8524-6488 ; School of Mathematical Sciences, Bohai University, Jinzhou , P. R. China *
Xiaofeng Wang

* Dopisni autor.

Sažetak

In this paper, the stability of an optimal eighth-order single-parameter King’s method is analyzed via fractal behavior. Under the Möbius conjugate map on the Riemann sphere, we study the complex dynamic behavior of this iterative method. Firstly, supported by studying the strange fixed points, we draw the corresponding stability planes. And through defining a unified plane, we also obtain the global stability plane of the strange fixed points. Secondly, with generating the dynamical planes of the iterative method corresponding to the given parameters in the complex plane, we can get a stable parameter family. Finally, by selecting the parameter c in the stable parameter family, we apply the corresponding iterative methods to carry out numerical experiments, which illustrate the effectiveness and stability of these iterative methods.

Ključne riječi

fractal behavior, complex dynamics, iterative methods, Mobius conjugacy, dynamical plane, nonlinear equations

Hrčak ID:

321249

URI

https://hrcak.srce.hr/321249

Datum izdavanja:

7.10.2024.

Posjeta: 81 *