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Open AccessArticle

New Iterative Methods for Solving Nonlinear Problems with One and Several Unknowns

1
Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
2
Multidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 Valencia, Spain
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(12), 296; https://doi.org/10.3390/math6120296
Received: 26 October 2018 / Revised: 23 November 2018 / Accepted: 25 November 2018 / Published: 1 December 2018
(This article belongs to the Special Issue Computational Methods in Analysis and Applications)
In this manuscript, a new type of study regarding the iterative methods for solving nonlinear models is presented. The goal of this work is to design a new fourth-order optimal family of two-step iterative schemes, with the flexibility through weight function/s or free parameter/s at both substeps, as well as small residual errors and asymptotic error constants. In addition, we generalize these schemes to nonlinear systems preserving the order of convergence. Regarding the applicability of the proposed techniques, we choose some real-world problems, namely chemical fractional conversion and the trajectory of an electron in the air gap between two parallel plates, in order to study the multi-factor effect, fractional conversion of species in a chemical reactor, Hammerstein integral equation, and a boundary value problem. Moreover, we find that our proposed schemes run better than or equal to the existing ones in the literature. View Full-Text
Keywords: nonlinear equations; local convergence analysis; order of convergence; Newton’s method; multi-point iterative methods; computational order of convergence nonlinear equations; local convergence analysis; order of convergence; Newton’s method; multi-point iterative methods; computational order of convergence
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MDPI and ACS Style

Behl, R.; Cordero, A.; Torregrosa, J.R.; Saleh Alshomrani, A. New Iterative Methods for Solving Nonlinear Problems with One and Several Unknowns. Mathematics 2018, 6, 296.

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