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A study of the local convergence of a fifth order iterative method

Author

Listed:
  • Sukjith Singh

    (Dr. B.R. Ambedkar Nationl Instutute of Technology)

  • Eulalia Martínez

    (Universitat Politècnica de València)

  • P. Maroju

    (Amrita Vishwa Vidhyapeetham)

  • Ramandeep Behl

    (King Abdulaziz University)

Abstract

We present a local convergence study of a fifth order iterative method to approximate a locally unique root of nonlinear equations. The analysis is discussed under the assumption that first order Fréchet derivative satisfies the Lipschitz continuity condition. Moreover, we consider the derivative free method that obtained through approximating the derivative with divided difference along with the local convergence study. Finally, we provide computable radii and error bounds based on the Lipschitz constant for both cases. Some of the numerical examples are worked out and compared the results with existing methods.

Suggested Citation

  • Sukjith Singh & Eulalia Martínez & P. Maroju & Ramandeep Behl, 2020. "A study of the local convergence of a fifth order iterative method," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(2), pages 439-455, June.
    • Handle: RePEc:spr:indpam:v:51:y:2020:i:2:d:10.1007_s13226-020-0409-5
    DOI: 10.1007/s13226-020-0409-5
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    References listed on IDEAS

    as
    1. Martínez, Eulalia & Singh, Sukhjit & Hueso, José L. & Gupta, Dharmendra K., 2016. "Enlarging the convergence domain in local convergence studies for iterative methods in Banach spaces," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 252-265.
    2. Singh, Sukhjit & Gupta, Dharmendra Kumar & Martínez, E. & Hueso, José L., 2016. "Semilocal and local convergence of a fifth order iteration with Fréchet derivative satisfying Hölder condition," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 266-277.
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