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Generating function method for constructing new iterations

Author

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  • Zhanlav, T.
  • Chuluunbaatar, O.
  • Ulziibayar, V.

Abstract

In this paper we propose a generating function method for constructing new two- and three-point iterations with p (3 ≤ p ≤ 8) order of convergence. This approach allows us to derive a new family of the optimal order iterative methods that include well known methods as special cases. The necessary and sufficient conditions for pth order convergence of the proposed iterations are given in terms of parameters τn and αn. We also propose some generating functions for τn and αn. We give the extension of a class of optimal fourth-order Jarratt’s type iterations with a≠23. We develop a unified representation of all optimal eighth-order methods. Several numerical results are given to demonstrate the efficiency and the performance of the presented methods and compare them with some other existing methods.

Suggested Citation

  • Zhanlav, T. & Chuluunbaatar, O. & Ulziibayar, V., 2017. "Generating function method for constructing new iterations," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 414-423.
    • Handle: RePEc:eee:apmaco:v:315:y:2017:i:c:p:414-423
    DOI: 10.1016/j.amc.2017.07.078
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    References listed on IDEAS

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    1. Chun, Changbum & Neta, Beny, 2015. "An analysis of a family of Maheshwari-based optimal eighth order methods," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 294-307.
    2. Sharma, Janak Raj & Arora, Himani, 2016. "A new family of optimal eighth order methods with dynamics for nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 924-933.
    3. Behl, Ramandeep & Cordero, Alicia & Motsa, Sandile S. & Torregrosa, Juan R., 2015. "Construction of fourth-order optimal families of iterative methods and their dynamics," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 89-101.
    4. Chun, Changbum & Neta, Beny, 2016. "Comparison of several families of optimal eighth order methods," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 762-773.
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    Cited by:

    1. Zhanlav, T. & Otgondorj, Kh., 2021. "Higher order Jarratt-like iterations for solving systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 395(C).

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