Ball convergence theorems and the convergence planes of an iterative method for nonlinear equations

被引：0
|
作者：
Alberto Magreñán Á. [1 ]
Argyros I.K. [2 ]
机构：
[1] Universidad Internacional de La Rioja, C/Gran Vía 41, Logroño, 26005, La Rioja
[2] Department of Mathematics Sciences Lawton, Cameron University, Lawton, 73505, OK
来源：
SeMA Journal | 2015年 / 71卷 / 1期
关键词：
Ball convergence; Convergence planes and nonlinear equations; Local convergence; Order of convergence;
D O I：
10.1007/s40324-015-0047-8
中图分类号：
学科分类号：
摘要：
We study the local convergence of a method presented by Cordero et al. of convergence order at least five to approximate a locally unique solution of a nonlinear equation. These studies show the convergence under hypotheses on the third derivative or even higher. The convergence in this study is shown under hypotheses on the first derivative. Hence, the applicability of the method is expanded. The dynamical analysis of this method is also studied. Finally, numerical examples are also provided to show that our results apply to solve equations in cases where earlier studies cannot apply. © 2015, Sociedad Española de Matemática Aplicada.
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页码：39 / 55
页数：16
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