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Efficient Multiplicative Calculus-Based Iterative Scheme for Nonlinear Engineering Applications

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  • Mudassir Shams

    (Faculty of Engineering, Free University of Bozen-Bolzano, 39100 Bolzano, Italy
    Department of Mathematics and Statistics, Riphah International University I-14, Islamabad 44000, Pakistan)

  • Nasreen Kausar

    (Department of Mathematics, Faculty of Arts and Science, Yildiz Technical University, Istanbul 34220, Türkiye)

  • Ioana Alexandra Șomîtcă

    (Department of Mathematics, Faculty of Automation and Computer Science, Technical University of Cluj-Napoca, Baritiu Street, no 26–28, 40027 Cluj-Napoca, Romania)

Abstract

It is essential to solve nonlinear equations in engineering, where accuracy and precision are critical. In this paper, a novel family of iterative methods for finding the simple roots of nonlinear equations based on multiplicative calculus is introduced. Based on theoretical research, a novel family of simple root-finding schemes based on multiplicative calculus has been devised, with a convergence order of seven. The symmetry in the pie graph of the convergence–divergence areas demonstrates that the method is stable and consistent when dealing with nonlinear engineering problems. An extensive examination of the numerical results of the engineering applications is presented in order to assess the effectiveness, stability, and consistency of the recently established method in comparison to current methods. The analysis includes the total number of functions and derivative evaluations per iteration, elapsed time, residual errors, local computational order of convergence, and error graphs, which demonstrate our method’s better convergence behavior when compared to other approaches.

Suggested Citation

  • Mudassir Shams & Nasreen Kausar & Ioana Alexandra Șomîtcă, 2024. "Efficient Multiplicative Calculus-Based Iterative Scheme for Nonlinear Engineering Applications," Mathematics, MDPI, vol. 12(22), pages 1-26, November.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3517-:d:1518549
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    References listed on IDEAS

    as
    1. Ali Özyapıcı & Zehra B. Sensoy & Tolgay Karanfiller, 2016. "Effective Root-Finding Methods for Nonlinear Equations Based on Multiplicative Calculi," Journal of Mathematics, Hindawi, vol. 2016, pages 1-7, October.
    2. Mudassir Shams & Bruno Carpentieri, 2023. "On Highly Efficient Fractional Numerical Method for Solving Nonlinear Engineering Models," Mathematics, MDPI, vol. 11(24), pages 1-30, December.
    3. David Levy, 1994. "Chaos theory and strategy: Theory, application, and managerial implications," Strategic Management Journal, Wiley Blackwell, vol. 15(S2), pages 167-178, June.
    4. Mudassir Shams & Nasreen Kausar & Cuauhtã‰Moc Samaniego & Praveen Agarwal & Shams Forruque Ahmed & Shaher Momani, 2023. "On Efficient Fractional Caputo-Type Simultaneous Scheme For Finding All Roots Of Polynomial Equations With Biomedical Engineering Applications," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(04), pages 1-15.
    5. Hossein Jafari & Roghayeh Moallem Ganji & Davood Domiri Ganji & Zakia Hammouch & Yusif S. Gasimov, 2023. "A Novel Numerical Method For Solving Fuzzy Variable-Order Differential Equations With Mittag-Leffler Kernels," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(04), pages 1-13.
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