An approximate solution for homogeneous boundary-value problems with slowly-varying coefficient matrices
type: Item
instance of: scholarly article
title: An approximate solution for homogeneous boundary-value problems with slowly-varying coefficient matrices
zbMATH Open document ID: 0814.65085
DOI: 10.1016/0898-1221(94)00153-7
author: V. Pereyra
publication date: 1994-11-06T00:00:00Z
review text: An approximate closed-form solution is obtained for linear homogeneous boundary-value problems with slowly-varying coefficient matrices. The derivation of the approximation solution is based on the freezing technique, which once solves the problem with the matrices ``frozen'' at a certain point and then relaxes it so as to have the independent variable. The error between the approximate and the exact solutions is given, and an upper bound on the norm of the error is obtained. This upper bound is proportional to the rate of change of the coefficient matrix of the problem. The proposed approximate solution is compared to the numerical solution in a two-point boundary-value problem. Good agreement is observed between two solutions when the rate of change of the matrix is small.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 34B05
zbMATH DE Number: 681874
zbMATH Keywords: error bound
zbMATH Keywords: approximate closed-form solution
zbMATH Keywords: linear homogeneous boundary-value problems
zbMATH Keywords: slowly-varying coefficient matrices
zbMATH Keywords: freezing technique
reviewed by: Taketomo Mitsui
MaRDI profile type: Publication
full work available at URL: 0898-1221(94)00153-7
OpenAlex ID: W2072412270
cites work: Q5559978
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cites work: &lt;tex&gt;L_infty&lt;/tex&gt;-stability criteria for interconnected systems using exponential weighting
cites work: Sufficient conditions for stability of linear time-varying systems
cites work: Response of linear slowly varying systems under external excitations
cites work: Matrix Analysis
published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 681874