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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| Published in: | Numerical functional analysis and optimization Vol. 12; no. 3-4; pp. 285 - 298 |
|---|---|
| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Philadelphia, PA
Marcel Dekker, Inc
01.01.1991
Taylor & Francis |
| Subjects: | |
| ISSN: | 0163-0563, 1532-2467 |
| Online Access: | Get full text |
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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. |
| Author_xml | – sequence: 1 givenname: B. surname: Büttgenbach fullname: Büttgenbach, B. organization: Lehrstuhl A für Mathematik – sequence: 2 givenname: H. surname: Esser fullname: Esser, H. organization: Institut für Geometrie and Praktische Mathematik , RWTH Aachen Templergrahen – sequence: 3 givenname: R. J. surname: Nessel 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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| Copyright | Copyright Taylor & Francis Group, LLC 1991 1992 INIST-CNRS |
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| Issue | 3-4 |
| Keywords | Two points boundary problem Error analysis Functional dependency Differential equation Green function Finite difference method |
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| References | Stoer J. (CIT0009) 1980 Sendov Bl. (CIT0008) 1988 Dickmeis W. (CIT0002) 1987; 89 CIT0001 Johnen H. (CIT0006) 1972; 9 CIT0005 CIT0004 Samarskij A. A. (CIT0007) 1984 Esser H. (CIT0003) 1974 Timan A. P. (CIT0010) 1963 |
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| Snippet | For linear two-point boundary value problems of ordinary differential equations, some convergence properties of approximate solutions Y
h
obtained by standard... |
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| StartPage | 285 |
| 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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