On dichotomy and well-conditioning in two-point boundary-value problems
type: Item
instance of: scholarly article
title: On dichotomy and well-conditioning in two-point boundary-value problems
zbMATH Open document ID: 0708.65076
DOI: 10.1016/0096-3003(90)90022-U
author: K. N. Murty
author: P. V. S. Lakshmi
published in: Applied Mathematics and Computation
publication date: 1990-01-01T00:00:00Z
review text: The boundary value problem \(P(t)y'(t)+Q(t)y(t)=f(t),\quad t\in [a,b]\) \(My(a)+Ny(b)=d,\) where \(M,N\in {\mathbb{R}}^{n\times n}\), \(d\in {\mathbb{R}}^ n\) and \(P,Q\in [L_ p(a,b)]^{n\times n}\), \(f\in [L_ p(a,b)]^ n\), \(1\leq p<\infty\) are given, is considered. The authors investigate the close relationship between the stability constants and the growth behavior of the fundamental matrix of this problem. It is also shown that the conditioning number is the right criterion to indicate possible error amplification of the perturbed boundary conditions.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34B05
zbMATH DE Number: 4164065
zbMATH Keywords: dichotomy
zbMATH Keywords: well-conditioning
zbMATH Keywords: stability constants
zbMATH Keywords: growth behavior
zbMATH Keywords: fundamental matrix
reviewed by: Józef Kalinowski
MaRDI profile type: Publication
cites work: The Stability of One-Step Schemes for First-Order Two-Pointv Boundary Value Problems
cites work: Dichotomies in stability theory
cites work: The Conditioning of Linear Boundary Value Problems
cites work: On Dichotomy and Well Conditioning in BVP
cites work: The Close Relationships between Methods for Solving Two-Point Boundary Value Problems
full work available at URL: 0096-3003(90)90022-u
OpenAlex ID: W2077642880
description: scientific article; zbMATH DE number 4164065