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Open AccessArticle

Generalized High-Order Classes for Solving Nonlinear Systems and Their Applications

1
Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, 26006 Logroño, Spain
2
Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2019, 7(12), 1194; https://doi.org/10.3390/math7121194
Received: 19 November 2019 / Revised: 29 November 2019 / Accepted: 2 December 2019 / Published: 5 December 2019
(This article belongs to the Special Issue Multipoint Methods for the Solution of Nonlinear Equations)
A generalized high-order class for approximating the solution of nonlinear systems of equations is introduced. First, from a fourth-order iterative family for solving nonlinear equations, we propose an extension to nonlinear systems of equations holding the same order of convergence but replacing the Jacobian by a divided difference in the weight functions for systems. The proposed GH family of methods is designed from this fourth-order family using both the composition and the weight functions technique. The resulting family has order of convergence 9. The performance of a particular iterative method of both families is analyzed for solving different test systems and also for the Fisher’s problem, showing the good performance of the new methods. View Full-Text
Keywords: nonlinear systems; iterative method; convergence; efficiency nonlinear systems; iterative method; convergence; efficiency
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MDPI and ACS Style

Chicharro, F.I.; Cordero, A.; Garrido, N.; Torregrosa, J.R. Generalized High-Order Classes for Solving Nonlinear Systems and Their Applications. Mathematics 2019, 7, 1194. https://doi.org/10.3390/math7121194

AMA Style

Chicharro FI, Cordero A, Garrido N, Torregrosa JR. Generalized High-Order Classes for Solving Nonlinear Systems and Their Applications. Mathematics. 2019; 7(12):1194. https://doi.org/10.3390/math7121194

Chicago/Turabian Style

Chicharro, Francisco I.; Cordero, Alicia; Garrido, Neus; Torregrosa, Juan R. 2019. "Generalized High-Order Classes for Solving Nonlinear Systems and Their Applications" Mathematics 7, no. 12: 1194. https://doi.org/10.3390/math7121194

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