The decomposition method for nonlinear dynamical systems
type: Item
instance of: scholarly article
title: The decomposition method for nonlinear dynamical systems
zbMATH Open document ID: 0625.34069
DOI: 10.1016/0022-247X(86)90223-4
author: G. Adomian
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: After asserting that all real problems are nonlinear, often strongly nonlinear, the author goes into considerations about deviations of the solutions from the actual physical behavior. He then introduces a decomposition method, of an operator-theoretic approach, in which general dynamical systems are viewed as being nonlinear and stochastic and described by nonlinear stochastic differential equations, systems of equations or partial differential equations. The method consists essentially in decomposing the solution process into additive components, the first being the solution of a simplified linear deterministic system and which takes into account the initial conditions, and each of the subsequent components is found in terms of a preceding one, thus ultimately in terms of the first. Several examples are given.
reviewed by: Ubiratan D'Ambrosio
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 35F20
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 37-XX
Mathematics Subject Classification ID: 93E03
zbMATH DE Number: 4015235
zbMATH Keywords: decomposition method
zbMATH Keywords: examples
MaRDI profile type: Publication
cites work: Inversion of nonlinear stochastic operators
cites work: Q3222535
cites work: Nonlinear equations with mixed derivatives
cites work: Convergent series solution of nonlinear equations
full work available at URL: 0022-247x(86)90223-4
OpenAlex ID: W2067247051
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description: scientific article; zbMATH DE number 4015235