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A New Adaptive Eleventh-Order Memory Algorithm for Solving Nonlinear Equations

Author

Listed:
  • Sunil Panday

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

  • Shubham Kumar Mittal

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

  • Carmen Elena Stoenoiu

    (Department of Electric Machines and Drives, Technical University of Cluj-Napoca, 26-28 Baritiu Str., 400027 Cluj-Napoca, Romania)

  • 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 introduce a novel three-step iterative algorithm with memory for finding the roots of nonlinear equations. The convergence order of an established eighth-order iterative method is elevated by transforming it into a with-memory variant. The improvement in the convergence order is achieved by introducing two self-accelerating parameters, calculated using the Hermite interpolating polynomial. As a result, the R-order of convergence for the proposed bi-parametric with-memory iterative algorithm is enhanced from 8 to 10.5208 . Notably, this enhancement in the convergence order is accomplished without the need for extra function evaluations. Moreover, the efficiency index of the newly proposed with-memory iterative algorithm improves from 1.5157 to 1.6011 . Extensive numerical testing across various problems confirms the usefulness and superior performance of the presented algorithm relative to some well-known existing algorithms.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:12:p:1809-:d:1412609
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    References listed on IDEAS

    as
    1. G Thangkhenpau & Sunil Panday & Shubham Kumar Mittal & Lorentz Jäntschi, 2023. "Novel Parametric Families of with and without Memory Iterative Methods for Multiple Roots of Nonlinear Equations," Mathematics, MDPI, vol. 11(9), pages 1-18, April.
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    Cited by:

    1. 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.

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