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New efficient methods for solving nonlinear systems of equations with arbitrary even order

Author

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  • Abbasbandy, Saeid
  • Bakhtiari, Parisa
  • Cordero, Alicia
  • Torregrosa, Juan R.
  • Lotfi, Taher

Abstract

In 2011, Khattri and Abbasbandy developed an optimal two-step Jarratt-like method for approximating simple roots of a nonlinear equation. We develop their method for solving nonlinear systems of equations. The main feature of the extended methods is that it uses only one LU factorization which preserves and reduces computational complexities. Following this aim, the suggested method is generalized in such a way that we increase the order of convergence but we do not need new LU factorization. Convergence and complexity analysis are provided rigorously. Using some small and large systems, applicability along with some comparisons are illustrated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:287-288:y:2016:i::p:94-103
    DOI: 10.1016/j.amc.2016.04.038
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    References listed on IDEAS

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    1. Khan, Waseem Asghar & Noor, Khalida Inayat & Bhatti, Kaleemulah & Ansari, Faryal Aijaz, 2015. "A new fourth order Newton-type method for solution of system of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 724-730.
    2. 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.
    3. Esmaeili, H. & Ahmadi, M., 2015. "An efficient three-step method to solve system of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1093-1101.
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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. 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.
    3. Malik Zaka Ullah & Ramandeep Behl & Ioannis K. Argyros, 2020. "Some High-Order Iterative Methods for Nonlinear Models Originating from Real Life Problems," Mathematics, MDPI, vol. 8(8), pages 1-17, July.
    4. Janak Raj Sharma & Deepak Kumar & Ioannis K. Argyros & Ángel Alberto Magreñán, 2019. "On a Bi-Parametric Family of Fourth Order Composite Newton–Jarratt Methods for Nonlinear Systems," Mathematics, MDPI, vol. 7(6), pages 1-27, May.
    5. Zhanlav, T. & Otgondorj, Kh., 2021. "Higher order Jarratt-like iterations for solving systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    6. Chun, Changbum & Neta, Beny, 2019. "Developing high order methods for the solution of systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 178-190.

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