Monotone iteration descretization algorithm for BVP's
type: Item
instance of: scholarly article
title: Monotone iteration descretization algorithm for BVP's
zbMATH Open document ID: 0662.65077
DOI: 10.1007/BF02238729
published in: Computing
publication date: 1989-01-01T00:00:00Z
review text: This paper deals with the following weakly nonlinear boundary value problem \(-u''+g(x,u(x))=0,\) \(u(a)=u(b)=0.\) By means of available estimations lower and upper solutions are generated. Authors replace the optimization by implementable estimations and propose a monotone iteration technique for the finite-dimensional problem in such a way that enclosures are obtained in each iteration step of the method. Finally, numerical realizations are given using interval arithmetic.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65G30
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 4082882
zbMATH Keywords: weakly nonlinear
zbMATH Keywords: lower and upper solutions
zbMATH Keywords: monotone iteration
zbMATH Keywords: interval arithmetic
author: M. A. Al-Zanaidi
author: Christian Grossmann
reviewed by: Rolf-Dieter Reiss
MaRDI profile type: Publication
cites work: Q4743663
cites work: Q4060307
cites work: Q4099123
cites work: Q4730711
cites work: Q3773193
cites work: Gleichmäßig einschließende Diskretisierungsverfahren für schwach nichtlineare Randwertaufgaben. (Uniformly enclosing discretization methods for weakly nonlinear boundary value problems)
cites work: Feedback Grid Generation via Monotone Discretization for Two-point Boundary-Value Problems
cites work: Q5628581
full work available at URL: https://doi.org/10.1007/bf02238729
OpenAlex ID: W189663389
description: scientific article; zbMATH DE number 4082882