Some new weighted eighth-order variants of Steffensen-King’s type family for solving nonlinear equations and its dynamics

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• 作者：V. Kanwar ; Raj Bala ; Munish Kansal
• 关键词：Nonlinear equations ; Multipoint methods ; Kung ; Traub conjecture ; Optimal efficiency index ; Basins of attraction
• 刊名：SeMA Journal
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：74
• 期：1
• 页码：75-90
• 全文大小：
• 刊物主题：Mathematics, general; Applications of Mathematics;
• 出版者：Springer Milan
• ISSN：2281-7875
• 卷排序：74

文摘

It is worth noting that there is a growing interest in obtaining iterative methods that are totally derivative free. In this paper, we present two new three-step eighth-order classes of Steffensen-King’s type methods for solving nonlinear equations numerically. In terms of computational cost, each member of the proposed families requires only four functional evaluations per full iteration to achieve optimal eighth-order convergence. A variety of concrete numerical examples and relevant results are extensively treated to verify the underlying theoretical development. Moreover, the presented basins of attraction also confirm that our proposed methods have better stability and robustness as compared to the other existing methods.