An error bound for approximate solutions of two-point boundary value problems
type: Item
instance of: scholarly article
title: An error bound for approximate solutions of two-point boundary value problems
zbMATH Open document ID: 0683.65068
DOI: 10.1007/BF02239753
published in: Computing
publication date: 1989-01-01T00:00:00Z
review text: This paper deals with error bounds for approximate solutions of the elliptic two-point boundary value problem \(-(py')'+qy=f,\quad y(0)=0,\quad y(1)=0.\) The error bounds presented here have two important advantages compared to those of \textit{E. C. Gartland} [SIAM J. Numer. Anal. 21, 84-100 (1984; Zbl 0561.65059)]: a) They can be applied to all kinds of approximate solutions and not only to those obtained by the Ritz method. b) The generalization to higher dimensions of the upper bound for the \(L_ 2\)-error norm poses no difficulties. Numerical experimentations with three different boundary value problems are presented.
reviewed by: Rolf-Dieter Reiss
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B05
zbMATH DE Number: 4119535
zbMATH Keywords: numerical examples
zbMATH Keywords: error bounds
zbMATH Keywords: Ritz method
author: John B. Kioustelidis
MaRDI profile type: Publication
cites work: Q5661106
cites work: Q3995065
cites work: Q3915947
cites work: Computable Pointwise Error Bounds and the Ritz Method in One Dimension
cites work: Collocation with Quadratic and Cubic Splines
cites work: \(L_ 2\)-error bounds for approximate solutions of elliptic partial differential equations with Dirichlet-boundary conditions
cites work: Q3851544
cites work: Q4100478
cites work: Q4098810
full work available at URL: https://doi.org/10.1007/bf02239753
OpenAlex ID: W2136160326
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description: scientific article; zbMATH DE number 4119535