An Optimal Family of Eighth-Order Iterative Methods with an Inverse Interpolatory Rational Function Error Corrector for Nonlinear Equations

被引：4
|
作者：
Kim, Young I. [1 ]
Behl, Ramandeep [2 ]
Motsa, Sandile S. [2 ,3 ]
机构：
[1] Dankook Univ, Dept Appl Math, Cheonan 330714, South Korea
[2] Univ KwaZulu Natal, Sch Math Stat & Comp Sci, Private Bag X01, ZA-3209 Pietermaritzburg, South Africa
[3] Univ Swaziland, Math Dept, Private Bag 4,M201, Kwaluseni, Swaziland
来源：
MATHEMATICAL MODELLING AND ANALYSIS | 2017年 / 22卷 / 03期
关键词：
nonlinear equations; simple roots; computational order of convergence; Newton's method; basins of attraction; OPTIMAL 8TH ORDER; CONVERGENCE; DYNAMICS;
D O I：
10.3846/13926292.2017.1309585
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The main motivation of this study is to propose an optimal scheme with an inverse interpolatory rational function error corrector in a general way that can be applied to any existing optimal multi-point fourth-order iterative scheme whose first sub step employs Newton's method to further produce optimal eighth-order iterative schemes. In addition, we also discussed the theoretical and computational properties of our scheme. Variety of concrete numerical experiments and basins of attraction are extensively treated to confirm the theoretical development.
引用
收藏
页码：321 / 336
页数：16
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