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Modified Potra–Pták Multi-step Schemes with Accelerated Order of Convergence for Solving Systems of Nonlinear Equations

1
Department of Mathematics, D.A.V. University, Sarmastpur, 144012 Jalandhar, India
2
Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, 46022 Valencia, Spain
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2019, 24(1), 3; https://doi.org/10.3390/mca24010003
Received: 29 November 2018 / Revised: 22 December 2018 / Accepted: 23 December 2018 / Published: 27 December 2018
(This article belongs to the Special Issue Mathematical Modelling in Engineering & Human Behaviour 2018)
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Abstract

In this study, an iterative scheme of sixth order of convergence for solving systems of nonlinear equations is presented. The scheme is composed of three steps, of which the first two steps are that of third order Potra–Pták method and last is weighted-Newton step. Furthermore, we generalize our work to derive a family of multi-step iterative methods with order of convergence 3 r + 6 , r = 0 , 1 , 2 , . The sixth order method is the special case of this multi-step scheme for r = 0 . The family gives a four-step ninth order method for r = 1 . As much higher order methods are not used in practice, so we study sixth and ninth order methods in detail. Numerical examples are included to confirm theoretical results and to compare the methods with some existing ones. Different numerical tests, containing academical functions and systems resulting from the discretization of boundary problems, are introduced to show the efficiency and reliability of the proposed methods. View Full-Text
Keywords: systems of nonlinear equations; iterative methods; Newton’s method; order of convergence; computational efficiency; basin of attraction systems of nonlinear equations; iterative methods; Newton’s method; order of convergence; computational efficiency; basin of attraction
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Arora, H.; Torregrosa, J.R.; Cordero, A. Modified Potra–Pták Multi-step Schemes with Accelerated Order of Convergence for Solving Systems of Nonlinear Equations. Math. Comput. Appl. 2019, 24, 3.

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