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An Optimal Derivative-Free Ostrowski’s Scheme for Multiple Roots of Nonlinear Equations

Author

Listed:
  • Ramandeep Behl

    (Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Samaher Khalaf Alharbi

    (Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Mathematics, College of Sciences and Arts in Al-Rass, Qassim University, Al-Rass 51921, Saudi Arabia)

  • Fouad Othman Mallawi

    (Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Mehdi Salimi

    (Department of Mathematics & Statistics, McMaster University, Hamilton, ON L8S 4L8, Canada
    Center for Dynamics, Faculty of Mathematics, Technische Universität Dresden, 01062 Dresden, Germany)

Abstract

Finding higher-order optimal derivative-free methods for multiple roots ( m ≥ 2 ) of nonlinear expressions is one of the most fascinating and difficult problems in the area of numerical analysis and Computational mathematics. In this study, we introduce a new fourth order optimal family of Ostrowski’s method without derivatives for multiple roots of nonlinear equations. Initially the convergence analysis is performed for particular values of multiple roots—afterwards it concludes in general form. Moreover, the applicability and comparison demonstrated on three real life problems (e.g., Continuous stirred tank reactor (CSTR), Plank’s radiation and Van der Waals equation of state) and two standard academic examples that contain the clustering of roots and higher-order multiplicity ( m = 100 ) problems, with existing methods. Finally, we observe from the computational results that our methods consume the lowest CPU timing as compared to the existing ones. This illustrates the theoretical outcomes to a great extent of this study.

Suggested Citation

  • Ramandeep Behl & Samaher Khalaf Alharbi & Fouad Othman Mallawi & Mehdi Salimi, 2020. "An Optimal Derivative-Free Ostrowski’s Scheme for Multiple Roots of Nonlinear Equations," Mathematics, MDPI, vol. 8(10), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1809-:d:429167
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    Citations

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    Cited by:

    1. Sunil Kumar & Ramandeep Behl & Azizah Alrajhi, 2023. "Efficient Fourth-Order Scheme for Multiple Zeros: Applications and Convergence Analysis in Real-Life and Academic Problems," Mathematics, MDPI, vol. 11(14), pages 1-16, July.
    2. Ramandeep Behl, 2022. "A Derivative Free Fourth-Order Optimal Scheme for Applied Science Problems," Mathematics, MDPI, vol. 10(9), pages 1-17, April.

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