Convergence of Adomian's method applied to nonlinear equations
type: Item
instance of: scholarly article
title: Convergence of Adomian's method applied to nonlinear equations
zbMATH Open document ID: 0822.65027
DOI: 10.1016/0895-7177(94)00163-4
author: K. Abbaoui
author: Yves Cherruault
published in: Mathematical and Computer Modelling
publication date: 1995-10-18T00:00:00Z
review text: The nonlinear equation \(f(x)= 0\) in \(\mathbb{R}\) is transformed into the form \(x= F(x)+ c\) (\(F\) is a nonlinear function, \(c\) is constant). The solution of the latter is calculated in the series form \(x= \sum^ \infty_{i= 0} x_ i\) and \(F(x)= \sum^ \infty_{i= 0} A_ i\), where \(A_ i\)'s are Adomian polynomials. The authors derive the convergence conditions and give the numerical examples.
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 722506
zbMATH Keywords: Adomian's method
zbMATH Keywords: nonlinear equation
zbMATH Keywords: convergence
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: 0895-7177(94)00163-4
OpenAlex ID: W2012098823
cites work: Application of decomposition to hyperbolic, parabolic, and elliptic partial differential equations
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description: scientific article; zbMATH DE number 722506