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A New High-Order Jacobian-Free Iterative Method with Memory for Solving Nonlinear Systems

Author

Listed:
  • Ramandeep Behl

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Alicia Cordero

    (Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain)

  • Juan R. Torregrosa

    (Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain)

  • Sonia Bhalla

    (Department of Mathematics, Chandigarh University, Mohali 140413, India)

Abstract

We used a Kurchatov-type accelerator to construct an iterative method with memory for solving nonlinear systems, with sixth-order convergence. It was developed from an initial scheme without memory, with order of convergence four. There exist few multidimensional schemes using more than one previous iterate in the very recent literature, mostly with low orders of convergence. The proposed scheme showed its efficiency and robustness in several numerical tests, where it was also compared with the existing procedures with high orders of convergence. These numerical tests included large nonlinear systems. In addition, we show that the proposed scheme has very stable qualitative behavior, by means of the analysis of an associated multidimensional, real rational function and also by means of a comparison of its basin of attraction with those of comparison methods.

Suggested Citation

  • Ramandeep Behl & Alicia Cordero & Juan R. Torregrosa & Sonia Bhalla, 2021. "A New High-Order Jacobian-Free Iterative Method with Memory for Solving Nonlinear Systems," Mathematics, MDPI, vol. 9(17), pages 1-16, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2122-:d:627284
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    References listed on IDEAS

    as
    1. Francisco I. Chicharro & Alicia Cordero & Neus Garrido & Juan R. Torregrosa, 2020. "Impact on Stability by the Use of Memory in Traub-Type Schemes," Mathematics, MDPI, vol. 8(2), pages 1-16, February.
    2. Neha Choubey & A. Cordero & J. P. Jaiswal & J. R. Torregrosa, 2018. "Dynamical Techniques for Analyzing Iterative Schemes with Memory," Complexity, Hindawi, vol. 2018, pages 1-13, June.
    3. Neha Choubey & A. Cordero & J. P. Jaiswal & J. R. Torregrosa, 2018. "Corrigendum to “Dynamical Techniques for Analyzing Iterative Schemes with Memory”," Complexity, Hindawi, vol. 2018, pages 1-1, September.
    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.
    Full references (including those not matched with items on IDEAS)

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