On solving boundary value problems for multi-scale systems using asymptotic approximations and multiple-shooting
type: Item
instance of: scholarly article
title: On solving boundary value problems for multi-scale systems using asymptotic approximations and multiple-shooting
zbMATH Open document ID: 0558.65056
DOI: 10.1007/BF01934918
author: Robert E. jun. O'Malley
author: R. M. M. Mattheij
published in: BIT
publication date: 1984-01-01T00:00:00Z
review text: The authors describe a method for obtaining a numerical solution of singularly perturbed boundary value problems for linear systems of ODE's whose solutions involve dynamics with multiple time scales. A technique to decouple different time scales using a Riccati transformation is presented. For the slow modes, regular perturbation expansion and multiple shooting strategies are combined to apply the technique of the first author and \textit{G. W. M. Staarink} [SIAM J. Sci. Stat. Comput. 5, 745-763 (1984; reviewed above)]. Fast modes, which are assumed to be significant only in endpoint layers, are computed after appropriate stretchings. Some numerical examples are given.
reviewed by: Taketomo Mitsui
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34E15
zbMATH DE Number: 3890648
zbMATH Keywords: multiple time scale
zbMATH Keywords: decoupling
zbMATH Keywords: Riccati transformation
zbMATH Keywords: regular perturbation expansion
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01934918
OpenAlex ID: W2049052401
description: scientific article; zbMATH DE number 3890648