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A family of Steffensen type methods with seventh-order convergence

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Abstract

In this paper, based on some known fourth-order Steffensen type methods, we present a family of three-step seventh-order Steffensen type iterative methods for solving nonlinear equations and nonlinear systems. For nonlinear systems, a development of the inverse first-order divided difference operator for multivariable function is applied to prove the order of convergence of the new methods. Numerical experiments with comparison to some existing methods are provided to support the underlying theory.

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Authors and Affiliations

  1. College of Sciences, Northeastern University, Shenyang, 110819, Liaoning, China

    Xiaofeng Wang & Tie Zhang

  2. Department of Mathematics, Bohai University, Jinzhou, 121013, Liaoning, China

    Xiaofeng Wang

Authors
  1. Xiaofeng Wang
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  2. Tie Zhang
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Correspondence to Xiaofeng Wang.

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Wang, X., Zhang, T. A family of Steffensen type methods with seventh-order convergence. Numer Algor 62, 429–444 (2013). https://doi.org/10.1007/s11075-012-9597-3

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  • DOI: https://doi.org/10.1007/s11075-012-9597-3

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