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New Family of Multi-Step Iterative Methods Based on Homotopy Perturbation Technique for Solving Nonlinear Equations

Author

Listed:
  • Huda J. Saeed

    (Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq)

  • Ali Hasan Ali

    (Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq
    Institute of Mathematics, University of Debrecen, Pf. 400, H-4002 Debrecen, Hungary)

  • Rayene Menzer

    (Institute of Mathematics, University of Debrecen, Pf. 400, H-4002 Debrecen, Hungary)

  • Ana Danca Poțclean

    (Department of Mathematics, Technical University of Cluj-Napoca, Str. Memorandumului nr. 28, 400114 Cluj-Napoca, Romania)

  • Himani Arora

    (Department of Mathematics, Guru Nanak Dev University, Amritsar 143005, India)

Abstract

This research aims to propose a new family of one-parameter multi-step iterative methods that combine the homotopy perturbation method with a quadrature formula for solving nonlinear equations. The proposed methods are based on a higher-order convergence scheme that allows for faster and more efficient convergence compared to existing methods. It aims also to demonstrate that the efficiency index of the proposed iterative methods can reach up to 4 3 ≈ 1.587 and 8 4 ≈ 1.681 , respectively, indicating a high degree of accuracy and efficiency in solving nonlinear equations. To evaluate the effectiveness of the suggested methods, several numerical examples including their performance are provided and compared with existing methods.

Suggested Citation

  • Huda J. Saeed & Ali Hasan Ali & Rayene Menzer & Ana Danca Poțclean & Himani Arora, 2023. "New Family of Multi-Step Iterative Methods Based on Homotopy Perturbation Technique for Solving Nonlinear Equations," Mathematics, MDPI, vol. 11(12), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2603-:d:1165697
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    References listed on IDEAS

    as
    1. Emad A. Az-Zo’bi & Kamel Al-Khaled & Amer Darweesh, 2019. "Numeric-Analytic Solutions for Nonlinear Oscillators via the Modified Multi-Stage Decomposition Method," Mathematics, MDPI, vol. 7(6), pages 1-13, June.
    2. Alim, Md. Abdul & Kawser, M. Abul, 2023. "Illustration of the homotopy perturbation method to the modified nonlinear single degree of freedom system," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
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    Cited by:

    1. Ramandeep Behl & Ioannis K. Argyros & Hashim Alshehri & Samundra Regmi, 2024. "Generalized Convergence for Multi-Step Schemes under Weak Conditions," Mathematics, MDPI, vol. 12(2), pages 1-15, January.

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