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Some new weighted eighth-order variants of Steffensen-King’s type family for solving nonlinear equations and its dynamics

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Abstract

It is worth noting that there is a growing interest in obtaining iterative methods that are totally derivative free. In this paper, we present two new three-step eighth-order classes of Steffensen-King’s type methods for solving nonlinear equations numerically. In terms of computational cost, each member of the proposed families requires only four functional evaluations per full iteration to achieve optimal eighth-order convergence. A variety of concrete numerical examples and relevant results are extensively treated to verify the underlying theoretical development. Moreover, the presented basins of attraction also confirm that our proposed methods have better stability and robustness as compared to the other existing methods.

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Acknowledgments

The authors are thankful to the anonymous reviewer for useful comments and suggestions towards the improvement of this paper.

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Authors and Affiliations

  1. University Institute of Engineering and Technology, Panjab University, Chandigarh, 160 014, India

    V. Kanwar & Munish Kansal

  2. Department of Mathematics, Government College Barwala, Panchkula, Haryana, 134 118, India

    Raj Bala

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  1. V. Kanwar
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  2. Raj Bala
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  3. Munish Kansal
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Correspondence to V. Kanwar.

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Kanwar, V., Bala, R. & Kansal, M. Some new weighted eighth-order variants of Steffensen-King’s type family for solving nonlinear equations and its dynamics. SeMA 74, 75–90 (2017). https://doi.org/10.1007/s40324-016-0081-1

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  • DOI: https://doi.org/10.1007/s40324-016-0081-1

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