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

Ramandeep Behl, Samaher Khalaf Alharbi, Fouad Othman Mallawi and Mehdi Salimi
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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
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

Mathematics, 2020, vol. 8, issue 10, 1-13

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.

Keywords: nonlinear equation; King–Traub conjecture; multiple root; optimal iterative method; efficiency index (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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