IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v355y2019icp516-536.html
   My bibliography  Save this article

A new time-efficient and convergent nonlinear solver

Author

Listed:
  • Abro, Hameer Akhtar
  • Shaikh, Muhammad Mujtaba

Abstract

Nonlinear equations arise in various fields of science and engineering. The present era of computational science – where one needs maximum achievement in minimum time – demands proposal of new and efficient iterative methods for solving nonlinear equations and systems. While the new methods are expected to be higher order convergent, the time efficiency and lesser computational information used are the top priorities. In this paper, we propose a new three-step iterative nonlinear solver for nonlinear equations and systems. The proposed method requires three evaluations of function and two evaluations of the first-order derivative per iteration. The proposed method is sixth order convergent, which is also proved theoretically. The performance of the proposed method is tested against other existing methods on the basis of error distributions, computational efficiency and CPU times. The numerical results on the application of the discussed methods on various nonlinear equations and systems, including an application problem related to combustion for a temperature of 3000 °C, show that the proposed method is comparable with existing methods with the main feature of the proposed method being its time-effectiveness.

Suggested Citation

  • Abro, Hameer Akhtar & Shaikh, Muhammad Mujtaba, 2019. "A new time-efficient and convergent nonlinear solver," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 516-536.
    • Handle: RePEc:eee:apmaco:v:355:y:2019:i:c:p:516-536
    DOI: 10.1016/j.amc.2019.03.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630031930205X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.03.012?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. Alicia Cordero & Esther Gómez & Juan R. Torregrosa, 2017. "Efficient High-Order Iterative Methods for Solving Nonlinear Systems and Their Application on Heat Conduction Problems," Complexity, Hindawi, vol. 2017, pages 1-11, January.
    2. Herceg, Djordje & Herceg, Dragoslav, 2015. "A family of methods for solving nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 882-895.
    3. Waseem, Muhammad & Noor, Muhammad Aslam & Noor, Khalida Inayat, 2016. "Efficient method for solving a system of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 134-146.
    4. Sharma, Janak Raj & Sharma, Rajni & Kalra, Nitin, 2015. "A novel family of composite Newton–Traub methods for solving systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 520-535.
    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. Sania Qureshi & Higinio Ramos & Abdul Karim Soomro, 2021. "A New Nonlinear Ninth-Order Root-Finding Method with Error Analysis and Basins of Attraction," Mathematics, MDPI, vol. 9(16), pages 1-19, August.

    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. 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.
    2. Zhanlav, T. & Otgondorj, Kh., 2021. "Higher order Jarratt-like iterations for solving systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    3. 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.
    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. Francisco I. Chicharro & Alicia Cordero & Neus Garrido & Juan R. Torregrosa, 2019. "Generalized High-Order Classes for Solving Nonlinear Systems and Their Applications," Mathematics, MDPI, vol. 7(12), pages 1-14, December.
    6. Beny Neta, 2021. "A Note on Traub’s Method for Systems of Nonlinear Equations," Mathematics, MDPI, vol. 9(23), pages 1-8, November.
    7. 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.
    8. 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:355:y:2019:i:c:p:516-536. 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.