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A Modified Ren’s Method with Memory Using a Simple Self-Accelerating Parameter

Author

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  • Xiaofeng Wang

    (School of Mathematics and Physics, Bohai University, Jinzhou 121000, China)

  • Qiannan Fan

    (School of Mathematics and Physics, Bohai University, Jinzhou 121000, China)

Abstract

In this paper, a self-accelerating type method is proposed for solving nonlinear equations, which is a modified Ren’s method. A simple way is applied to construct a variable self-accelerating parameter of the new method, which does not increase any computational costs. The highest convergence order of new method is 2 + 6 ≈ 4.4495 . Numerical experiments are made to show the performance of the new method, which supports the theoretical results.

Suggested Citation

  • Xiaofeng Wang & Qiannan Fan, 2020. "A Modified Ren’s Method with Memory Using a Simple Self-Accelerating Parameter," Mathematics, MDPI, vol. 8(4), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:540-:d:342141
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    References listed on IDEAS

    as
    1. Lotfi, Taher & Assari, Paria, 2015. "New three- and four-parametric iterative with memory methods with efficiency index near 2," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 1004-1010.
    2. Ullah, M. Zaka & Kosari, S. & Soleymani, F. & Haghani, F. Khaksar & S. Al-Fhaid, A., 2016. "A super-fast tri-parametric iterative method with memory," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 486-491.
    3. Soleymani, F. & Lotfi, T. & Tavakoli, E. & Khaksar Haghani, F., 2015. "Several iterative methods with memory using self-accelerators," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 452-458.
    4. Campos, Beatriz & Cordero, Alicia & Torregrosa, Juan R. & Vindel, Pura, 2015. "A multidimensional dynamical approach to iterative methods with memory," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 701-715.
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