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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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    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)

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