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Open AccessArticle

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

Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, 26006 Logroño, Spain
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;
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.

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