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

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• 作者：Janak Raj Sharma^a ; ^{jrshira@yahoo.co.in} ; Ioannis K. Argyros^b ; ^{iargyros@cameron.edu} ; Deepak Kumar^a ; ^{deepak.babbi@gmail.com}
• 关键词：Nonlinear equations ; Multipoint methods ; Rational Hermite interpolation ; Optimal convergence
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 May 2017
• 年：2017
• 卷：449
• 期：2
• 页码：994-1014
• 全文大小：447 K
• 卷排序：449

文摘

We develop a class of n  -point iterative methods with optimal 2n2n order of convergence for solving nonlinear equations. Newton's second order and Ostrowski's fourth order methods are special cases corresponding to n=1n=1 and n=2n=2. Eighth and sixteenth order methods that correspond to n=3n=3 and n=4n=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)(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.