ON INVERSE ITERATION PROCESS FOR FINDING ALL ROOTS OF NONLINEAR EQUATIONS WITH APPLICATIONS

Mudassir Shams, Naila Rafiq, Nasreen Kausar, Praveen Agarwal, Nazir Ahmad Mir and Nasser El-Kanj
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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

FRACTALS (fractals), 2022, vol. 30, issue 10, 1-14

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.

Keywords: Fractional Nonlinear Equations; Iterative Methods; Derivative Free Simultaneous Method; Basins of Attractions; Computational Efficiency; Engineering Applications (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22402654

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