Two-point boundary value problems associated with first order nonlinear difference system -- existence and uniqueness
type: Item
instance of: scholarly article
title: Two-point boundary value problems associated with first order nonlinear difference system -- existence and uniqueness
zbMATH Open document ID: 0935.39001
DOI: 10.1016/S0096-3003(98)00021-6
author: K. Appert
published in: Applied Mathematics and Computation
publication date: 2000-01-03T00:00:00Z
review text: This paper examines first-order matrix difference equations of the form \[ T(n+1) = A(n)T(n)B(n) + F(n,T(n)) \] in which \(A\), \(B\), \(F\) and \(T\) are square matrices, with \(F\) Lipschitz. A variation of parameters formula is obtained for the solutions, in terms of the fundamental matrices of the associated systems \(\Phi(n+1) = A(n) \Phi(n)\) and \(\Psi(n+1) = B(n)^*\Psi(n)B(n)\). The authors prove that certain associated two-point boundary value problems are uniquely solvable, by using a modified QR algorithm of \textit{R. H. Bartels} and \textit{G. W. Stewart} [Commun. ACM 15, No. 9, 820--826 (1972; Zbl 1372.65121)].
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 65Q05
zbMATH DE Number: 1311076
zbMATH Keywords: matrix difference equations
zbMATH Keywords: first-order nonlinear difference system
zbMATH Keywords: variation of parameters formula
zbMATH Keywords: two-point boundary value problems
zbMATH Keywords: QR algorithm
reviewed by: Marco Marletta
MaRDI profile type: Publication
cites work: Q4845420
cites work: Algorithm 432 [C2]: Solution of the matrix equation AX + XB = C [F4]
cites work: On multipoint boundary value problems for discrete equations
cites work: Theory of difference equations: Numerical methods and applications
cites work: Discrete and continuous boundary problems
cites work: Solution of the Equation $AX + XB = C$ by Inversion of an $M \times M$ or $N \times N$ Matrix
cites work: Explicit Solutions of Linear Matrix Equations
full work available at URL: s0096-3003(98)00021-6
OpenAlex ID: W2073981495
description: scientific article; zbMATH DE number 1311076