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Open AccessArticle

Some Real-Life Applications of a Newly Constructed Derivative Free Iterative Scheme

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Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
2
Center for Dynamics and Institute for Analysis, Department of Mathematics, Technische Universität Dresden, 01062 Dresden, Germany
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Department of Law, Economics and Human Sciences, University Mediterranea of Reggio Calabria, 89125 Reggio Calabria, Italy
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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
5
MEDAlics, Research Center at Università per Stranieri Dante Alighieri, 89125 Reggio Calabria, Italy
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(2), 239; https://doi.org/10.3390/sym11020239
Received: 1 January 2019 / Revised: 24 January 2019 / Accepted: 28 January 2019 / Published: 15 February 2019
(This article belongs to the Special Issue Symmetry with Operator Theory and Equations)
In this study, we present a new higher-order scheme without memory for simple zeros which has two major advantages. The first one is that each member of our scheme is derivative free and the second one is that the present scheme is capable of producing many new optimal family of eighth-order methods from every 4-order optimal derivative free scheme (available in the literature) whose first substep employs a Steffensen or a Steffensen-like method. In addition, the theoretical and computational properties of the present scheme are fully investigated along with the main theorem, which demonstrates the convergence order and asymptotic error constant. Moreover, the effectiveness of our scheme is tested on several real-life problems like Van der Waal’s, fractional transformation in a chemical reactor, chemical engineering, adiabatic flame temperature, etc. In comparison with the existing robust techniques, the iterative methods in the new family perform better in the considered test examples. The study of dynamics on the proposed iterative methods also confirms this fact via basins of attraction applied to a number of test functions. View Full-Text
Keywords: scalar equations; computational convergence order; Steffensen’s method; basins of attraction scalar equations; computational convergence order; Steffensen’s method; basins of attraction
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MDPI and ACS Style

Behl, R.; Salimi, M.; Ferrara, M.; Sharifi, S.; Alharbi, S.K. Some Real-Life Applications of a Newly Constructed Derivative Free Iterative Scheme. Symmetry 2019, 11, 239.

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