Least square approximation of a nonlinear ordinary differential equation
type: Item
instance of: scholarly article
title: Least square approximation of a nonlinear ordinary differential equation
zbMATH Open document ID: 0855.65066
DOI: 10.1016/0898-1221(96)00032-6
author: Ovide Arino
author: Tayeb Benouaz
publication date: 1996-08-11T00:00:00Z
review text: The subject of the paper is an optimal linearization method for nonlinear ordinary differential equations. Results concerning an earlier proposed approximation are presented. The main results stipulate that the proposed approximation is of order two with respect to the initial value, and is generally of the same order as the nonlinearity. Necessary and sufficient conditions are given for uniqueness of the elements of the sequence determined in the course of the optimal approximation. Several examples are included showing satisfactory adequacy of approximate results compared to the exact ones.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 915114
zbMATH Keywords: numerical examples
zbMATH Keywords: mean square convergence
zbMATH Keywords: stability
zbMATH Keywords: linearization method
zbMATH Keywords: nonlinear ordinary differential equations
reviewed by: Dana Petcu
MaRDI profile type: Publication
full work available at URL: 0898-1221(96)00032-6
OpenAlex ID: W2002655881
Wikidata QID: Q115362880
cites work: Q4835298
cites work: Q3754503
cites work: Q3753881
cites work: Q4524880
cites work: Q3262547
published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 915114