The modified decomposition method for solving nonlinear algebraic equations
type: Item
instance of: scholarly article
title: The modified decomposition method for solving nonlinear algebraic equations
zbMATH Open document ID: 1031.65067
DOI: 10.1016/S0096-3003(01)00215-6
author: Salah M. El-Sayed
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: This paper proposes an exact method for solving nonlinear algebraic equations in one unknown. The method consists of expressing the solution of the nonlinear equation as an infinite series, the terms of which are generalized polynomials. The author develops the technique proposed before by \textit{K. Abbaoui} and \textit{Y. Cherruault} [Math. Comput. Modelling 20, 69-73 (1994; Zbl 0822.65027)] and by \textit{R. Z. Ouedraogo, Y. Cherruault} and \textit{K. Abbaoui} [Kybernetes 29, 1298-1305 (2000; Zbl 0994.65054)]. The absolute convergence of the series giving the solution of the equation is proved under some constraints. Two numerical examples are presented which suggest that the method proposed here is more accurate than the methods from literature.
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 1861232
zbMATH Keywords: nonlinear algebraic equations
zbMATH Keywords: Adomian's decomposition method
zbMATH Keywords: Adomian polynomial
zbMATH Keywords: comparison of methods
zbMATH Keywords: convergence
zbMATH Keywords: numerical examples
reviewed by: Iulian Coroian
MaRDI profile type: Publication
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full work available at URL: s0096-3003(01)00215-6
OpenAlex ID: W2045441394
description: scientific article; zbMATH DE number 1861232