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New efficient multipoint iterative methods for solving nonlinear systems

Author

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  • Rostamy, Davoud
  • Bakhtiari, Parisa

Abstract

It is attempted to put forward a new multipoint iterative method for approximating solutions of nonlinear systems. The main feature of the extended methods is that it uses only one LU factorization which preserves and reduces computational complexities. Moreover, the first step is designed in such a way that in most cases singularity of the denominator is avoided. Therefore, we try to generalize the suggested method so that we can increase the order of convergence from four to six and eight, but we do not need any new LU factorization. Also, we justify this advantage of the convergence analysis versus some numerical methods with different examples.

Suggested Citation

  • Rostamy, Davoud & Bakhtiari, Parisa, 2015. "New efficient multipoint iterative methods for solving nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 350-356.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:350-356
    DOI: 10.1016/j.amc.2015.05.087
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    Citations

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    Cited by:

    1. Ramandeep Behl & Ioannis K. Argyros, 2020. "A New Higher-Order Iterative Scheme for the Solutions of Nonlinear Systems," Mathematics, MDPI, vol. 8(2), pages 1-21, February.
    2. Cordero, Alicia & Leonardo-Sepúlveda, Miguel A. & Torregrosa, Juan R. & Vassileva, María P., 2024. "Increasing in three units the order of convergence of iterative methods for solving nonlinear systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 509-522.
    3. Abbasbandy, Saeid & Bakhtiari, Parisa & Cordero, Alicia & Torregrosa, Juan R. & Lotfi, Taher, 2016. "New efficient methods for solving nonlinear systems of equations with arbitrary even order," Applied Mathematics and Computation, Elsevier, vol. 287, pages 94-103.
    4. Deepak Kumar & Ioannis K. Argyros & Janak Raj Sharma, 2018. "Convergence Ball and Complex Geometry of an Iteration Function of Higher Order," Mathematics, MDPI, vol. 7(1), pages 1-13, December.
    5. Hessah Faihan Alqahtani & Ramandeep Behl & Munish Kansal, 2019. "Higher-Order Iteration Schemes for Solving Nonlinear Systems of Equations," Mathematics, MDPI, vol. 7(10), pages 1-14, October.
    6. Sharma, Janak Raj & Sharma, Rajni & Bahl, Ashu, 2016. "An improved Newton–Traub composition for solving systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 98-110.
    7. Marcos Tostado-Véliz & Salah Kamel & Francisco Jurado & Francisco J. Ruiz-Rodriguez, 2021. "On the Applicability of Two Families of Cubic Techniques for Power Flow Analysis," Energies, MDPI, vol. 14(14), pages 1-15, July.
    8. Narang, Mona & Bhatia, Saurabh & Kanwar, V., 2016. "New two-parameter Chebyshev–Halley-like family of fourth and sixth-order methods for systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 394-403.

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