IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i15p2595-d871362.html
   My bibliography  Save this article

Multi-Step Quantum Numerical Techniques for Finding the Solutions of Nonlinear Equations

Author

Listed:
  • Kamsing Nonlaopon

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

  • Awais Gul Khan

    (Department of Mathematics, Government College University, Faisalabad 38000, Pakistan)

  • Farah Ameen

    (Department of Mathematics, Government College University, Faisalabad 38000, Pakistan)

  • Muhammad Uzair Awan

    (Department of Mathematics, Government College University, Faisalabad 38000, Pakistan)

  • Clemente Cesarano

    (Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy)

Abstract

In this paper, we analyze the q -iterative schemes to determine the roots of nonlinear equations by applying the decomposition technique with Simpson’s 1 3 -rule in the setting of q-calculus. We discuss the convergence analysis of our suggested iterative methods. To check the efficiency and performance, we also compare our main outcomes with some well known techniques existing in the literature.

Suggested Citation

  • Kamsing Nonlaopon & Awais Gul Khan & Farah Ameen & Muhammad Uzair Awan & Clemente Cesarano, 2022. "Multi-Step Quantum Numerical Techniques for Finding the Solutions of Nonlinear Equations," Mathematics, MDPI, vol. 10(15), pages 1-17, July.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2595-:d:871362
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/15/2595/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/15/2595/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Faisal Ali & Waqas Aslam & Imran Khalid & Akbar Nadeem & Antonio Di Crescenzo, 2020. "Iteration Methods with an Auxiliary Function for Nonlinear Equations," Journal of Mathematics, Hindawi, vol. 2020, pages 1-15, October.
    2. Manar A. Alqudah & Pshtiwan Othman Mohammed & Thabet Abdeljawad, 2020. "Solution of Singular Integral Equations via Riemann–Liouville Fractional Integrals," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-8, September.
    3. Noor, Muhammad Aslam & Waseem, Muhammad & Noor, Khalida Inayat & Ali, Muhammad Aamir, 2015. "New iterative technique for solving nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1115-1125.
    4. Pshtiwan Othman Mohammed & José António Tenreiro Machado & Juan L. G. Guirao & Ravi P. Agarwal, 2021. "Adomian Decomposition and Fractional Power Series Solution of a Class of Nonlinear Fractional Differential Equations," Mathematics, MDPI, vol. 9(9), pages 1-18, May.
    5. Faisal Ali & Waqas Aslam & Kashif Ali & Muhammad Adnan Anwar & Akbar Nadeem, 2018. "New Family of Iterative Methods for Solving Nonlinear Models," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-12, April.
    6. Noor, Muhammad Aslam & Waseem, Muhammad & Noor, Khalida Inayat, 2015. "New iterative technique for solving a system of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 446-466.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Waseem, Muhammad & Noor, Muhammad Aslam & Noor, Khalida Inayat, 2016. "Efficient method for solving a system of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 134-146.
    2. Munish Kansal & Alicia Cordero & Sonia Bhalla & Juan R. Torregrosa, 2020. "Memory in a New Variant of King’s Family for Solving Nonlinear Systems," Mathematics, MDPI, vol. 8(8), pages 1-15, July.
    3. Sabermahani, Sedigheh & Ordokhani, Yadollah & Rahimkhani, Parisa, 2023. "Application of generalized Lucas wavelet method for solving nonlinear fractal-fractional optimal control problems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    4. Chein-Shan Liu & Essam R. El-Zahar & Chih-Wen Chang, 2023. "A Two-Dimensional Variant of Newton’s Method and a Three-Point Hermite Interpolation: Fourth- and Eighth-Order Optimal Iterative Schemes," Mathematics, MDPI, vol. 11(21), pages 1-21, November.
    5. Noor, Muhammad Aslam & Waseem, Muhammad & Noor, Khalida Inayat, 2015. "New iterative technique for solving a system of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 446-466.
    6. Xiaoming Wang & Shehbaz Ahmad Javed & Abdul Majeed & Mohsin Kamran & Muhammad Abbas, 2022. "Investigation of Exact Solutions of Nonlinear Evolution Equations Using Unified Method," Mathematics, MDPI, vol. 10(16), pages 1-17, August.
    7. Shengfeng Li & Xiaobin Liu & Xiaofang Zhang, 2019. "A Few Iterative Methods by Using [1, n ]-Order Padé Approximation of Function and the Improvements," Mathematics, MDPI, vol. 7(1), pages 1-14, January.
    8. Pshtiwan Othman Mohammed & José António Tenreiro Machado & Juan L. G. Guirao & Ravi P. Agarwal, 2021. "Adomian Decomposition and Fractional Power Series Solution of a Class of Nonlinear Fractional Differential Equations," Mathematics, MDPI, vol. 9(9), pages 1-18, May.
    9. Leonard Dăuş & Ghiocel Groza & Marilena Jianu, 2022. "Full Hermite Interpolation and Approximation in Topological Fields," Mathematics, MDPI, vol. 10(11), pages 1-17, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2595-:d:871362. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.