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Derivative-Free Families of With- and Without-Memory Iterative Methods for Solving Nonlinear Equations and Their Engineering Applications

Author

Listed:
  • Ekta Sharma

    (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)

  • Shubham Kumar Mittal

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

  • Dan-Marian Joița

    (Chemistry Doctoral School, Babeş-Bolyai University, 400084 Cluj, Romania
    Department of Physics and Chemistry, Technical University of Cluj-Napoca, B.-dul Muncii nr. 103-105, 400641 Cluj-Napoca, Romania)

  • Lavinia Lorena Pruteanu

    (Department of Chemistry and Biology, North University Center at Baia Mare, Technical University of Cluj-Napoca, 430122 Baia Mare, Romania)

  • Lorentz Jäntschi

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

Abstract

In this paper, we propose a new fifth-order family of derivative-free iterative methods for solving nonlinear equations. Numerous iterative schemes found in the existing literature either exhibit divergence or fail to work when the function derivative is zero. However, the proposed family of methods successfully works even in such scenarios. We extended this idea to memory-based iterative methods by utilizing self-accelerating parameters derived from the current and previous approximations. As a result, we increased the convergence order from five to ten without requiring additional function evaluations. Analytical proofs of the proposed family of derivative-free methods, both with and without memory, are provided. Furthermore, numerical experimentation on diverse problems reveals the effectiveness and good performance of the proposed methods when compared with well-known existing methods.

Suggested Citation

  • Ekta Sharma & Sunil Panday & Shubham Kumar Mittal & Dan-Marian Joița & Lavinia Lorena Pruteanu & Lorentz Jäntschi, 2023. "Derivative-Free Families of With- and Without-Memory Iterative Methods for Solving Nonlinear Equations and Their Engineering Applications," Mathematics, MDPI, vol. 11(21), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4512-:d:1272415
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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.
    2. T. Lotfi & F. Soleymani & Z. Noori & A. Kılıçman & F. Khaksar Haghani, 2014. "Efficient Iterative Methods with and without Memory Possessing High Efficiency Indices," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-9, September.
    3. Beny Neta, 2021. "A New Derivative-Free Method to Solve Nonlinear Equations," Mathematics, MDPI, vol. 9(6), pages 1-5, March.
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