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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Vydané v:Numerical functional analysis and optimization Ročník 12; číslo 3-4; s. 285 - 298
Hlavní autori: Büttgenbach, B., Esser, H., Nessel, R. J.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Philadelphia, PA Marcel Dekker, Inc 01.01.1991
Taylor & Francis
Predmet:
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
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Popis
Shrnutí: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