Boundary conditions and their transfer for differential-algebraic equations of index 1
type: Item
instance of: scholarly article
title: Boundary conditions and their transfer for differential-algebraic equations of index 1
zbMATH Open document ID: 0855.34019
DOI: 10.1016/0898-1221(96)00047-8
author: Yanyan Li
publication date: 1997-02-16T00:00:00Z
review text: The purpose of this paper is to describe the linear subspace of the differential-algebraic equation (1) \(Ay' + By = 0\) defined by the condition (2) \(C^T y(x_0) = 0\), where \(A,B \in C^1 (I,L (\mathbb{R}^n))\), \(C \in L(\mathbb{R}^m, \mathbb{R}^n)\), \(I \subset \mathbb{R}\) is a closed interval, \(x_0 \in I\) and equation (1) is index 1-tractable with \(\dim \text{Im} A = r < n\). To obtain the adjoint or dual of (1), i.e., (3) \((A^T \eta)' - B^T \eta = 0\), the author applies the reduction method. Equation (3) transfers the condition (2) along the interval I. Above the theoretical interest, this study is important for elaborating numerical methods to solve to boundary value problems (because a boundary value problem for a differential-algebraic equation may be reduced to that of a regular ordinary differential equation).
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34A09
zbMATH DE Number: 915129
zbMATH Keywords: differential-algebraic equation
zbMATH Keywords: adjoint
zbMATH Keywords: dual
zbMATH Keywords: reduction method
zbMATH Keywords: boundary value problems
reviewed by: Vasile Iftode
MaRDI profile type: Publication
full work available at URL: 0898-1221(96)00047-8
OpenAlex ID: W2077250233
cites work: Linear subspaces for linear DAEs of index 1
cites work: Q3766743
cites work: Duality, observability, and controllability for linear time-varying descriptor systems
cites work: Basic properties of some differential-algebraic equations
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 915129