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Open AccessArticle

A New Optimal Family of Schröder’s Method for Multiple Zeros

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Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
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Department of Law, Economics and Human Sciences & Decisions Lab, University Mediterranea of Reggio Calabria, 89125 Reggio Calabria, Italy
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Center for Dynamics and Institute for Analysis, Department of Mathematics, Technische Universität Dresden, 01062 Dresden, Germany
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ICRIOS—The Invernizzi Centre for Research on Innovation, Organization, Strategy and Entrepreneurship, Department of Management and Technology, Bocconi University, Via Sarfatti, 25, 20136 Milano, Italy
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Author to whom correspondence should be addressed.
Mathematics 2019, 7(11), 1076; https://doi.org/10.3390/math7111076
Received: 25 August 2019 / Revised: 23 October 2019 / Accepted: 24 October 2019 / Published: 8 November 2019
(This article belongs to the Special Issue Computational Methods in Analysis and Applications)
Here, we suggest a high-order optimal variant/modification of Schröder’s method for obtaining the multiple zeros of nonlinear uni-variate functions. Based on quadratically convergent Schröder’s method, we derive the new family of fourth -order multi-point methods having optimal convergence order. Additionally, we discuss the theoretical convergence order and the properties of the new scheme. The main finding of the present work is that one can develop several new and some classical existing methods by adjusting one of the parameters. Numerical results are given to illustrate the execution of our multi-point methods. We observed that our schemes are equally competent to other existing methods. View Full-Text
Keywords: efficiency index; nonlinear uni-variate functions; Schröder’s method; optimal order of convergence efficiency index; nonlinear uni-variate functions; Schröder’s method; optimal order of convergence
MDPI and ACS Style

Behl, R.; Alsolami, A.J.; Pansera, B.A.; Al-Hamdan, W.M.; Salimi, M.; Ferrara, M. A New Optimal Family of Schröder’s Method for Multiple Zeros. Mathematics 2019, 7, 1076.

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