Adomian's method of decomposition: Critical review and examples of failure
type: Item
instance of: scholarly article
title: Adomian's method of decomposition: Critical review and examples of failure
zbMATH Open document ID: 0645.65084
DOI: 10.1016/0377-0427(88)90008-8
author: B. George
published in: Journal of Computational and Applied Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Adomian's method of decomposition is considered in application to initial-boundary value problems for the one space-dimensional spatially homogeneous heat conduction equation. It is shown that the fundamental equation of the method is well-defined only for certain restricted types of boundary conditions. Within the class of such boundary conditions, examples are given such that the fundamental equation fails to have a unique solution, and such that the sequence produced by iteration of this equation is divergent. The latter is a counterexample to \textit{G. Adomian}'s assertion of convergence [J. Math. Anal. Appl. 113, 202-209 (1986; Zbl 0606.35037)].
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 4052953
zbMATH Keywords: Adomian's method of decomposition
zbMATH Keywords: heat conduction equation
MaRDI profile type: Publication
full work available at URL: 0377-0427(88)90008-8
OpenAlex ID: W2091308106
cites work: Q3928754
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description: scientific article; zbMATH DE number 4052953