Monotone iterative technique for initial-value problems of nonlinear singular discrete systems
type: Item
instance of: scholarly article
title: Monotone iterative technique for initial-value problems of nonlinear singular discrete systems
zbMATH Open document ID: 1159.65101
author: Peiguang Wang
author: Jing Zhang
published in: Journal of Computational and Applied Mathematics
publication date: 2008-10-22T00:00:00Z
review text: The authors consider the initial-value problem (IVP) for nonsingular discrete systems of the following type \[ Ax(k+1)=f(x,x(k)),\quad x(0)=C_0, \tag{1} \] where \(k\in M\), \(A\) is a real singular \(n\times n\) matrix, \(x(k) \in\mathbb R^n\), \(C_0\in\mathbb R^n\) is a constant vector and \(f\in C[M\times\mathbb R^n,\mathbb R^n]\), \(M=\{0,1,2,\dots\}\). They are seeking for lower and upper solutions for the IVP for the singular discrete system (1) and obtain monotone sequences which converge to extremal solutions of (1). An existence theorem and extremal solutions based on a monotone iterative technique are proved and a numerical example is also provided.
reviewed by: Otu Vaarmann
Mathematics Subject Classification ID: 65Q05
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 5355639
zbMATH Keywords: initial-value problems
zbMATH Keywords: iteration methods
zbMATH Keywords: upper and lower solutions
zbMATH Keywords: nonlinear singular discrete systems
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: j.cam.2007.10.002
OpenAlex ID: W2021757607
cites work: Q3852479
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DOI: 10.1016/J.CAM.2007.10.002
description: scientific article; zbMATH DE number 5355639