On the sharpness of error bounds in connection with finite difference schemes on uniform grids for boundary value problems of ordinary differential equations

For linear two-point boundary value problems of ordinary differential equations, some convergence properties of approximate solutions Y h obtained by standard finite difference schemes on uniform grids are discussed. By means of discrete Green's functions a representation of the error Y h -Y in...

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Bibliographic Details
Published in:Numerical functional analysis and optimization Vol. 12; no. 3-4; pp. 285 - 298
Main Authors: Büttgenbach, B., Esser, H., Nessel, R. J.
Format: Journal Article
Language:English
Published: Philadelphia, PA Marcel Dekker, Inc 01.01.1991
Taylor & Francis
Subjects:
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Sciences and techniques of general use
Two points boundary problem
Error analysis
Functional dependency
Differential equation
Green function
Finite difference method
ISSN:0163-0563, 1532-2467
Online Access:Get full text
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Summary:For linear two-point boundary value problems of ordinary differential equations, some convergence properties of approximate solutions Y h obtained by standard finite difference schemes on uniform grids are discussed. By means of discrete Green's functions a representation of the error Y h -Y in functional dependence on the exact solution Y is employed to prove the sharpness (with regard to the order) of well-known error estimates in terms of moduli of smoothness of derivatives of Y.
ISSN:0163-0563
1532-2467
DOI:10.1080/01630569108816429