Original scientific paper

An optimal sixteenth order family of methods for solving nonlinear equations and their basins of attraction

Dejan Ćebić ; Faculty of Mining and Geology, University of Belgrade, Belgrade, Serbia
Nebojša M Ralević Ralević ; Faculty of Engineering, University of Novi Sad, Novi Sad, Serbia
Marina Marčeta ; Faculty of Engineering, University of Novi Sad, Novi Sad, Serbia

Abstract

We propose a new family of iterative methods for finding the simple roots of nonlinear equation. The proposed method is four-point method with convergence order 16, which consists of four steps: the Newton step, an optional fourth order iteration scheme, an optional eighth order iteration scheme and the step constructed using the divided difference. By reason of the new iteration scheme requiring four function evaluations and one first derivative evaluation per iteration, the method satisfies the optimality criterion in the sense of Kung-Traub's conjecture and achieves a high efficiency index $16^{1/5} \approx 1.7411$. Computational results support theoretical analysis and confirm the efficiency.
The basins of attraction of the new presented algorithms are also compared to the existing methods with encouraging results.

Keywords

nonlinear equation; sixteenth-order convergence; optimal methods; divided differences; basins of attraction

Hrčak ID:

244284

URI

https://hrcak.srce.hr/244284

Publication date:

29.9.2020.

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