A biparametric extension of King’s fourth-order methods and their dynamics

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• 作者：Young Hee Geum^a ; ^{conpana@empas.com" class="auth_mail" title="E-mail the corresponding author} ; Young Ik Kim ; ^a ; ^{yikbell@yahoo.co.kr" class="auth_mail" title="E-mail the corresponding author} ; Á ; . Alberto Magre&ntilde ; á ; n^b ; ^{alberto.magrenan@unir.net" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Parameter space ; Error corrector ; Dynamical plane ; King&rsquo ; s fourth-order method
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：5 May 2016
• 年：2016
• 卷：282
• 期：Complete
• 页码：254-275
• 全文大小：3959 K

文摘

A class of two-point quartic-order simple-zero finders and their dynamics are investigated in this paper by extending King’s fourth-order family of methods. With the introduction of an error corrector having a weight function dependent on a function-to-function ratio, higher-order convergence is obtained. Through a variety of test equations, numerical experiments strongly support the theory developed in this paper. In addition, relevant dynamics of the proposed methods is successfully explored for a prototype quadratic polynomial as well as parameter spaces and dynamical planes.