IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v287-288y2016ip94-103.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316302880
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.04.038?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Ramandeep Behl & Alicia Cordero & Juan R. Torregrosa & Ali Saleh Alshomrani, 2018. "New Iterative Methods for Solving Nonlinear Problems with One and Several Unknowns," Mathematics, MDPI, vol. 6(12), pages 1-17, December.
    3. 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.
    4. 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.
    5. Ramandeep Behl & Ioannis K. Argyros & Jose Antonio Tenreiro Machado, 2020. "Ball Comparison between Three Sixth Order Methods for Banach Space Valued Operators," Mathematics, MDPI, vol. 8(5), pages 1-12, April.
    6. 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.
    7. 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.
    8. Bahl, Ashu & Cordero, Alicia & Sharma, Rajni & R. Torregrosa, Juan, 2019. "A novel bi-parametric sixth order iterative scheme for solving nonlinear systems and its dynamics," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 147-166.
    9. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:287-288:y:2016:i::p:94-103. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.