Numerical-analytic methods for differential-algebraic systems
type: Item
instance of: scholarly article
title: Numerical-analytic methods for differential-algebraic systems
zbMATH Open document ID: 0997.34001
DOI: 10.1023/A:1015688922724
published in: Acta Mathematica Hungarica
publication date: 2002-11-03T00:00:00Z
review text: Sufficient conditions are obtained for existence and uniqueness of solutions of differential-algebraic systems with boundary conditions of the form \[ \begin{gathered} x'=f(t,x,y),\;t\in I=[0, T],\;Ax(0)+Bx(T)=D,\\ y=g(t,x,y),\quad t\in I,\end{gathered} \] where \(f\in C(I\times \mathbb{R}^p\times \mathbb{R}^q,\mathbb{R}^p)\), \(g\in C(I\times \mathbb{R}^p\times \mathbb{R}^q,\mathbb{R}^q)\), and \(A_{p\times p}\), \(B_{p\times p}\) and \(D_{p\times 1}\) are given constant matrices. The numerical-analytic method combined with the comparison method is used to get these results under the assumption that \(f\) and \(g\) satisfy Lipschitz conditions with respect to the last two variables.
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34A45
Mathematics Subject Classification ID: 34B99
zbMATH DE Number: 1822375
zbMATH Keywords: numerical-analytic method
zbMATH Keywords: differential-algebraic systems
zbMATH Keywords: comparison method
zbMATH Keywords: retardations
zbMATH Keywords: existence and uniqueness of solutions
author: Tadeusz Jankowski
MaRDI profile type: Publication
full work available at URL: a:1015688922724
OpenAlex ID: W1682353999
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description: scientific article; zbMATH DE number 1822375