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Open AccessArticle

An Optimal Fourth Order Derivative-Free Numerical Algorithm for Multiple Roots

Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Sangrur 148106, India
Department of Mathematics, Chandigarh University, Gharuan, Mohali 140413, India
Section of Mathematics, International Telematic University UNINETTUNO, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
Department of Mathematics, Anand International College of Engineering, Jaipur 303012, Rajasthan, India
International Center for Basic and Applied Sciences, Jaipur 302029, India
Department of Mathematics, Harish-Chandra Research Institute, Allahabad 211 019, India
Department of Mathematics, Netaji Subhas University of Technology Dwarka Sector-3, Dwarka, Delhi 110078, India
Department of Mathematics, Huzhou University, Huzhou 313000, China
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, China
Author to whom correspondence should be addressed.
Symmetry 2020, 12(6), 1038;
Received: 25 May 2020 / Revised: 17 June 2020 / Accepted: 19 June 2020 / Published: 21 June 2020
(This article belongs to the Special Issue Ordinary and Partial Differential Equations: Theory and Applications)
A plethora of higher order iterative methods, involving derivatives in algorithms, are available in the literature for finding multiple roots. Contrary to this fact, the higher order methods without derivatives in the iteration are difficult to construct, and hence, such methods are almost non-existent. This motivated us to explore a derivative-free iterative scheme with optimal fourth order convergence. The applicability of the new scheme is shown by testing on different functions, which illustrates the excellent convergence. Moreover, the comparison of the performance shows that the new technique is a good competitor to existing optimal fourth order Newton-like techniques. View Full-Text
Keywords: nonlinear functions; multiple zeros; derivative-free iteration; convergence nonlinear functions; multiple zeros; derivative-free iteration; convergence
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Kumar, S.; Kumar, D.; Sharma, J.R.; Cesarano, C.; Agarwal, P.; Chu, Y.-M. An Optimal Fourth Order Derivative-Free Numerical Algorithm for Multiple Roots. Symmetry 2020, 12, 1038.

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