A biparametric family of optimally convergent sixteenth-order multipoint methods with their fourth-step weighting function as a sum of a rational and a generic two-variable function

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article

Geum, Young Hee¹  Kim, Young Ik¹ 

[1] Dankook Univ, Dept Appl Math, Cheonan 330714, South Korea

关键词: Eighth-order;    Sixteenth-order;    Optimal order;    Biparametric family;    Asymptotic error constant;    Efficiency index;   

DOI  :  10.1016/j.cam.2011.01.003

来源: Elsevier

【 摘 要 】

A biparametric family of four-step multipoint iterative methods of order sixteen to numerically solve nonlinear equations are developed and their convergence properties are investigated. The efficiency indices of these methods are all found to be 16(1/5) approximate to 1.741101, being optimally consistent with the conjecture of Kung-Traub. Numerical examples as well as comparison with existing methods developed by Kung-Traub and Neta are demonstrated to confirm the developed theory in this paper. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

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