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On Inverse Iteration Process For Finding All Roots Of Nonlinear Equations With Applications

Author

Listed:
  • MUDASSIR SHAMS

    (Department of Mathematics and Statistics, Riphah International University, Islamabad 44000, Pakistan)

  • NAILA RAFIQ

    (��Department of Mathematics, NUML, Islamabad, Pakistan)

  • NASREEN KAUSAR

    (��Department of Mathematics, Yildiz Technical University, Faculty of Arts and Science, Esenler 34210, Istanbul, Turkey)

  • PRAVEEN AGARWAL

    (�Department of Mathematics, Anand International, College of Engineering, Jaipur 303012, Rajasthan, India¶Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, 117198 Moscow, Russian Federation∥Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE)

  • NAZIR AHMAD MIR

    (��Department of Mathematics, NUML, Islamabad, Pakistan)

  • NASSER EL-KANJ

    (*College of Business Administration, American University of the Middle East, Egaila 54200, Kuwait)

Abstract

In this work, we construct a new family of inverse iterative numerical technique for extracting all roots of nonlinear equation simultaneously. Convergence analysis verifies that the proposed family of methods has local 10th-order convergence. Among the test models investigated are blood rheology, a fractional nonlinear equation model, fluid permeability in biogels, and beam localization models. In comparison to other methods, the family of inverse simultaneous iterative techniques gets initial estimations to exact roots within a given tolerance while using less function evaluations in each iterative step. Numerical results, basins of attraction for fractional nonlinear equation, residual graphs are presented in detail for the simultaneous iterative techniques. The newly developed simultaneous iterative techniques were thoroughly investigated and proven to be efficient, robust, and authentic in their domain.

Suggested Citation

  • Mudassir Shams & Naila Rafiq & Nasreen Kausar & Praveen Agarwal & Nazir Ahmad Mir & Nasser El-Kanj, 2022. "On Inverse Iteration Process For Finding All Roots Of Nonlinear Equations With Applications," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(10), pages 1-14, December.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:10:n:s0218348x22402654
    DOI: 10.1142/S0218348X22402654
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