On the local convergence and the dynamics of Chebyshev-Halley methods with six and eight order of convergence

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• 作者：Á ; . Alberto Magre&ntilde ; á ; n^a ; ^{alberto.magrenan@unir.net" class="auth_mail" title="E-mail the corresponding author} ; Ioannis K. Argyros^b ; ^{iargyros@cameron.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：65D10 ; 65D99 ; 65G99 ; 90C30
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：15 May 2016
• 年：2016
• 卷：298
• 期：Complete
• 页码：236-251
• 全文大小：1857 K

文摘

We study the local convergence of Chebyshev–Halley methods with six and eight order of convergence to approximate a locally unique solution of a nonlinear equation. In Sharma (2015) (see Theorem 1, p. 121) the convergence of the method was shown under hypotheses reaching up to the third derivative. The convergence in this study is shown under hypotheses on the first derivative. Hence, the applicability of the method is expanded. The dynamics of these methods are also studied. Finally, numerical examples examining dynamical planes are also provided in this study to solve equations in cases where earlier studies cannot apply.