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| HAL: hal-00705730, version 1 |
| DOI: 10.1007/s10543-010-0278-0 |
| Detailed view |  Export this paper |
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| BIT Numerical Mathematics 50, 4 (2010) 843-862 |
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| Error estimate and extrapolation of a quadrature formula derived from a quartic spline quasi-interpolant |
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| Paul Sablonnière 1Driss Sbibih 2 |
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| (2010) |
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| In this paper we analyze a quadrature rule based on integrating a C 3 quartic spline quasi-interpolant on a bounded interval which has been introduced in Sablonnière (Rend. Semin. Mat. Univ. Pol. Torino 63(3):107-118, 2005). By studying the sign structure of its associated Peano kernel we derive an explicit formula of the quadrature error with an approximation order O(h 6). A comparison of this rule with the composite Boole's and the three-point Gauss-Legendre rules is given. We also compare the Nyström methods associated with the above quadrature formulae for solving the linear Fredholm integral equation of the second kind. Then, by combining the proposed rule with composite Boole's rule, we construct a new quadrature rule of order O(h 7). All the obtained results are illustrated by several numerical tests. |
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| 1: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 2: | Université Mohammed 1er, Maroc (MRC-UMIS-MI) |
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Université Mohammed 1er OUJDA |
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| Analyse numérique |
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| Subject | : | Mathematics/Numerical Analysis |
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| Quadrature formula – Quasi-interpolation – Nyström method – Fredholm integral equation |
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| hal-00705730, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00705730 | |
| oai:hal.archives-ouvertes.fr:hal-00705730 | |
| From: Marie-Annick Guillemer | |
| Submitted on: Friday, 8 June 2012 10:54:18 | |
| Updated on: Friday, 8 June 2012 10:54:18 | |
