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

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Abstract

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.

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Authors and Affiliations

  1. Department of Information and Electronics, Hangzhou Radio and TV University, Hangzhou, 310012, Zhejiang, People’s Republic of China

    Hongmin Ren

  2. Department of Mathematics, Zhejiang University, Hangzhou, 310027, Zhejiang, People’s Republic of China

    Qingbiao Wu & Weihong Bi

Authors
  1. Hongmin Ren
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  2. Qingbiao Wu
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  3. Weihong Bi
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Correspondence to Hongmin Ren.

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Ren, H., Wu, Q. & Bi, W. New variants of Jarratt’s method with sixth-order convergence. Numer Algor 52, 585–603 (2009). https://doi.org/10.1007/s11075-009-9302-3

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  • DOI: https://doi.org/10.1007/s11075-009-9302-3

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Mathematics Subject Classifications (2000)