Computable error bounds for collocation methods
This paper deals with error bounds for numerical solutions of linear ordinary differential equations by global or piecewise polynomial collocation methods which are based on consideration of the involved differential operator, related matrices and the residual. It is shown that significant improveme...
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| Format: | Article |
| Language: | English |
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Wiley
1995-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171295000123 |
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| _version_ | 1832554072791580672 |
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| author | A. H. Ahmed |
| author_facet | A. H. Ahmed |
| author_sort | A. H. Ahmed |
| collection | DOAJ |
| description | This paper deals with error bounds for numerical solutions of linear ordinary
differential equations by global or piecewise polynomial collocation methods which are based on
consideration of the involved differential operator, related matrices and the residual. It is shown
that significant improvement may be obtained if direct bounds for the error in the solution are
considered. The practical implementation of the theory is illustrated by a selection of numerical
examples. |
| format | Article |
| id | doaj-art-30bf65542f7649bb8448a65314e747ce |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1995-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-30bf65542f7649bb8448a65314e747ce2025-02-03T05:52:21ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251995-01-01181899610.1155/S0161171295000123Computable error bounds for collocation methodsA. H. Ahmed0Department of Mathematics, Ash-Sharq University, Khartoum, SudanThis paper deals with error bounds for numerical solutions of linear ordinary differential equations by global or piecewise polynomial collocation methods which are based on consideration of the involved differential operator, related matrices and the residual. It is shown that significant improvement may be obtained if direct bounds for the error in the solution are considered. The practical implementation of the theory is illustrated by a selection of numerical examples.http://dx.doi.org/10.1155/S0161171295000123 |
| spellingShingle | A. H. Ahmed Computable error bounds for collocation methods International Journal of Mathematics and Mathematical Sciences |
| title | Computable error bounds for collocation methods |
| title_full | Computable error bounds for collocation methods |
| title_fullStr | Computable error bounds for collocation methods |
| title_full_unstemmed | Computable error bounds for collocation methods |
| title_short | Computable error bounds for collocation methods |
| title_sort | computable error bounds for collocation methods |
| url | http://dx.doi.org/10.1155/S0161171295000123 |
| work_keys_str_mv | AT ahahmed computableerrorboundsforcollocationmethods |