Decomposition methods: A new proof of convergence
type: Item
instance of: scholarly article
title: Decomposition methods: A new proof of convergence
zbMATH Open document ID: 0805.65057
DOI: 10.1016/0895-7177(93)90233-O
author: Yves Cherruault
author: G. Adomian
published in: Mathematical and Computer Modelling
publication date: 1995-02-02T00:00:00Z
review text: The authors consider nonlinear equations of the form (*) \(u-N(u)=f\) where \(N\) and \(f\), respectively, are operator and function given in convenient spaces. They construct a solution of (*) in the form (+) \(u=\sum^ \infty_{i=0} u_ i\) where the \(u_ i\) are successively defined. A convergence proof of the series (+) is proposed and the error of the truncated series of (+) is estimated. No application is given. [Remark: The proof is not very distinct; in particular, the space in which the proof is valid is not stated].
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 575782
zbMATH Keywords: nonlinear operator equation
zbMATH Keywords: error estimate
zbMATH Keywords: convergence
reviewed by: Walter Petry
MaRDI profile type: Publication
cites work: Convergence of Adomian's Method
cites work: New results for convergence of Adomian's method applied to integral equations
cites work: Q4040348
cites work: Q4289027
cites work: An Efficient Methodology for the Physical Sciences
full work available at URL: 0895-7177(93)90233-o
OpenAlex ID: W2049446621
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description: scientific article; zbMATH DE number 575782