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Open AccessArticle

A New Higher-Order Iterative Scheme for the Solutions of Nonlinear Systems

by Ramandeep Behl 1,† and Ioannis K. Argyros 2,*,†
1
Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
2
Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(2), 271; https://doi.org/10.3390/math8020271
Received: 23 January 2020 / Revised: 9 February 2020 / Accepted: 10 February 2020 / Published: 18 February 2020
Many real-life problems can be reduced to scalar and vectorial nonlinear equations by using mathematical modeling. In this paper, we introduce a new iterative family of the sixth-order for a system of nonlinear equations. In addition, we present analyses of their convergences, as well as the computable radii for the guaranteed convergence of them for Banach space valued operators and error bounds based on the Lipschitz constants. Moreover, we show the applicability of them to some real-life problems, such as kinematic syntheses, Bratu’s, Fisher’s, boundary value, and Hammerstein integral problems. We finally wind up on the ground of achieved numerical experiments, where they perform better than other competing schemes. View Full-Text
Keywords: iterative schemes; Newton’s method; Banach space; order of convergence iterative schemes; Newton’s method; Banach space; order of convergence
MDPI and ACS Style

Behl, R.; Argyros, I.K. A New Higher-Order Iterative Scheme for the Solutions of Nonlinear Systems. Mathematics 2020, 8, 271.

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