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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Veröffentlicht in:Numerical functional analysis and optimization Jg. 12; H. 3-4; S. 285 - 298
Hauptverfasser: Büttgenbach, B., Esser, H., Nessel, R. J.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia, PA Marcel Dekker, Inc 01.01.1991
Taylor & Francis
Schlagworte:
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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Abstract 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.
AbstractList 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.
Author Esser, H.
Büttgenbach, B.
Nessel, R. J.
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  fullname: Nessel, R. J.
  organization: Lehrstuhl A für Mathematik
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Cites_doi 10.1007/978-1-4757-5592-3
10.1080/01630568108816077
10.1515/9783112713952
10.1007/BF01403858
10.1080/01630568908816292
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Issue 3-4
Keywords Two points boundary problem
Error analysis
Functional dependency
Differential equation
Green function
Finite difference method
Language English
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Taylor & Francis
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CIT0001
Johnen H. (CIT0006) 1972; 9
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CIT0004
Samarskij A. A. (CIT0007) 1984
Esser H. (CIT0003) 1974
Timan A. P. (CIT0010) 1963
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– volume-title: The Averaged Moduli of Smoothness
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SubjectTerms Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Sciences and techniques of general use
Title On the sharpness of error bounds in connection with finite difference schemes on uniform grids for boundary value problems of ordinary differential equations
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