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A new time-efficient and convergent nonlinear solver.

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Title: A new time-efficient and convergent nonlinear solver.
Authors: Abro, Hameer Akhtar1 (AUTHOR) hameer.abro@faculty.muet.edu.pk, Shaikh, Muhammad Mujtaba1,2 (AUTHOR) mujtaba.shaikh@faculty.muet.edu.pk
Source: Applied Mathematics & Computation. Aug2019, Vol. 355, p516-536. 21p.
Subjects: Nonlinear equations, Nonlinear systems, Achievement motivation, Iterative methods (Mathematics), Maxima & minima, Combustion
Abstract: 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. [ABSTRACT FROM AUTHOR]
Copyright of Applied Mathematics & Computation is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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PubType: Academic Journal
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  Data: <searchLink fieldCode="DE" term="%22Nonlinear+equations%22">Nonlinear equations</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+systems%22">Nonlinear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Achievement+motivation%22">Achievement motivation</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Maxima+%26+minima%22">Maxima & minima</searchLink><br /><searchLink fieldCode="DE" term="%22Combustion%22">Combustion</searchLink>
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  Data: 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. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Applied Mathematics & Computation is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.amc.2019.03.012
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 21
        StartPage: 516
    Subjects:
      – SubjectFull: Nonlinear equations
        Type: general
      – SubjectFull: Nonlinear systems
        Type: general
      – SubjectFull: Achievement motivation
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
        Type: general
      – SubjectFull: Maxima & minima
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      – SubjectFull: Combustion
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              Text: Aug2019
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