New variants of Jarratt's method with sixth-order convergence

作者：Ren Hongmin^*; Wu Qingbiao; Bi Weihong

来源：Numerical Algorithms, 2009, 52(4): 585-603.

DOI：10.1007/s11075-009-9302-3

• Nonlinear equations
• Iterative methods
• Jarratt's method
• Order of convergence
• Two-variable Taylor expansion formula

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.

• 出版日期2009-12
• 单位浙江大学