Next Article in Journal
Analysis of Homotopy Decomposition Varieties in Quotient Topological Spaces
Next Article in Special Issue
Boundary Layer Flow and Heat Transfer of Al2O3-TiO2/Water Hybrid Nanofluid over a Permeable Moving Plate
Previous Article in Journal
Concrete Based Jeffrey Nanofluid Containing Zinc Oxide Nanostructures: Application in Cement Industry
Previous Article in Special Issue
New Uniform Motion and Fermi–Walker Derivative of Normal Magnetic Biharmonic Particles in Heisenberg Space
Open AccessArticle

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

1
Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Sangrur 148106, India
2
Department of Mathematics, Chandigarh University, Gharuan, Mohali 140413, India
3
Section of Mathematics, International Telematic University UNINETTUNO, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
4
Department of Mathematics, Anand International College of Engineering, Jaipur 303012, Rajasthan, India
5
International Center for Basic and Applied Sciences, Jaipur 302029, India
6
Department of Mathematics, Harish-Chandra Research Institute, Allahabad 211 019, India
7
Department of Mathematics, Netaji Subhas University of Technology Dwarka Sector-3, Dwarka, Delhi 110078, India
8
Department of Mathematics, Huzhou University, Huzhou 313000, China
9
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; https://doi.org/10.3390/sym12061038
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
Show Figures

Figure 1

MDPI and ACS Style

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.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop