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New iterative technique for solving nonlinear equations

Author

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  • Noor, Muhammad Aslam
  • Waseem, Muhammad
  • Noor, Khalida Inayat
  • Ali, Muhammad Aamir

Abstract

Various problems of pure and applied sciences can be studied in the unified frame work of the nonlinear equations. In this paper, a new family of iterative methods for solving nonlinear equations is developed by using a new decomposition technique. The convergence of the proposed methods is proved. It is shown that the new family contains several well-known iterative methods as special case. For the implementation and performance of the new methods, a nonlinear equation arising in the population model and another one arising in the motion of a particle on inclined plane is solved.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:1115-1125
    DOI: 10.1016/j.amc.2015.05.129
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.

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