On a general class of optimal order multipoint methods for solving nonlinear equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:449

Article

Sharma, Janak Raj¹  Argyros, Ioannis K.²  Kumar, Deepak¹ 

[1] Sant Longowal Inst Engn & Technol, Dept Math, Longowal 148106, Punjab, India

[2] Cameron Univ, Dept Math, Lawton, OK 73505 USA

关键词: Nonlinear equations;    Multipoint methods;    Rational Hermite interpolation;    Optimal convergence;   

DOI  :  10.1016/j.jmaa.2016.12.051

来源: Elsevier

【 摘 要 】

We develop a class of n-point iterative methods with optimal 2(n) order of convergence for solving nonlinear equations. Newton's second order and Ostrowski's fourth order methods are special cases corresponding to n = 1 and n = 2. Eighth and sixteenth order methods that correspond to n = 3 and n = 4 of the class are special cases of the eighth and sixteenth order methods proposed by Sharma et al. [25]. The methodology is based on employing the previously obtained (n - 1)-step scheme and modifying the n-th step by using rational Hermite interpolation. Unlike that of existing higher order techniques the proposed technique is attractive since it leads to a simple implementation. Local convergence analysis is provided to show that the iterations are locally well defined and convergent. Theoretical results are verified through numerical experimentations. The performance is also compared with already established methods in literature. It is observed that new algorithms are more accurate than existing counterparts and very effective in high precision computations. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free