New variants of Jarratt鈥檚 method with sixth-order convergence
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- 作者：Hongmin Ren ; Qingbiao Wu and Weihong Bi
- 关键词：Nonlinear equations ; Iterative methods ; Jarratt’ ; s method ; Order of convergence ; Two ; variable Taylor expansion formula
- 刊名：Numerical Algorithms
- 出版时间：December, 2009
- 出版年：2009
- 期刊代码：48_10171398
- 类别：mt
- 卷：52
- 期：4
- 页码：585-603
- 数据来源：sp
摘要
In this paper, by using the two-variable Taylor expansion formula, we introduce some new variants of Jarratt’s method with sixth-order convergence for solving univariate nonlinear equations. The proposed methods contain some recent improvements of Jarratt’s method. Furthermore, a new variant of Jarratt’s method with sixth-order convergence for solving systems of nonlinear equations is proposed only with an additional evaluation for the involved function, and not requiring the computation of new inverse. Numerical comparisons are made to show the performance of the presented methods.