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Enhanced Ninth-Order Memory-Based Iterative Technique for Efficiently Solving Nonlinear Equations

Author

Listed:
  • Shubham Kumar Mittal

    (Department of Mathematics, National Institute of Technology Manipur, Langol, Imphal 795004, Manipur, India)

  • Sunil Panday

    (Department of Mathematics, National Institute of Technology Manipur, Langol, Imphal 795004, Manipur, India)

  • Lorentz Jäntschi

    (Department of Physics and Chemistry, Technical University of Cluj-Napoca, 103-105 Muncii Blvd., 400641 Cluj-Napoca, Romania)

Abstract

In this article, we present a novel three-step with-memory iterative method for solving nonlinear equations. We have improved the convergence order of a well-known optimal eighth-order iterative method by converting it into a with-memory version. The Hermite interpolating polynomial is utilized to compute a self-accelerating parameter that improves the convergence order. The proposed uni-parametric with-memory iterative method improves its R-order of convergence from 8 to 8.8989 . Additionally, no more function evaluations are required to achieve this improvement in convergence order. Furthermore, the efficiency index has increased from 1.6818 to 1.7272 . The proposed method is shown to be more effective than some well-known existing methods, as shown by extensive numerical testing on a variety of problems.

Suggested Citation

  • Shubham Kumar Mittal & Sunil Panday & Lorentz Jäntschi, 2024. "Enhanced Ninth-Order Memory-Based Iterative Technique for Efficiently Solving Nonlinear Equations," Mathematics, MDPI, vol. 12(22), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3490-:d:1516596
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    References listed on IDEAS

    as
    1. Sunil Panday & Shubham Kumar Mittal & Carmen Elena Stoenoiu & Lorentz Jäntschi, 2024. "A New Adaptive Eleventh-Order Memory Algorithm for Solving Nonlinear Equations," Mathematics, MDPI, vol. 12(12), pages 1-14, June.
    2. Chein-Shan Liu & Chih-Wen Chang, 2024. "New Memory-Updating Methods in Two-Step Newton’s Variants for Solving Nonlinear Equations with High Efficiency Index," Mathematics, MDPI, vol. 12(4), pages 1-22, February.
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