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

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Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
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Department of Mathematics, College of Sciences and Arts in Al-Rass, Qassim University, Al-Rass 51921, Saudi Arabia
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Department of Mathematics & Statistics, McMaster University, Hamilton, ON L8S 4L8, Canada
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Center for Dynamics, Faculty of Mathematics, Technische Universität Dresden, 01062 Dresden, Germany
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(10), 1809; https://doi.org/10.3390/math8101809
Received: 13 September 2020 / Revised: 1 October 2020 / Accepted: 10 October 2020 / Published: 16 October 2020
Finding higher-order optimal derivative-free methods for multiple roots (m2) 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. View Full-Text
Keywords: nonlinear equation; King–Traub conjecture; multiple root; optimal iterative method; efficiency index nonlinear equation; King–Traub conjecture; multiple root; optimal iterative method; efficiency index
MDPI and ACS Style

Behl, R.; Alharbi, S.K.; Mallawi, F.O.; Salimi, M. An Optimal Derivative-Free Ostrowski’s Scheme for Multiple Roots of Nonlinear Equations. Mathematics 2020, 8, 1809.

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