Discrete artificial boundary conditions for the linearized Korteweg–de Vries equation |
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| Authors: | C. Besse M. Ehrhardt I. Lacroix‐Violet |
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| Affiliation: | 1. Institut de Mathématiques de Toulouse UMR5219, Université de Toulouse, CNRS, UPS IMT, Toulouse Cedex 9, France;2. Bergische Universit?t Wuppertal, Fakult?t Mathematik und Naturwissenschaften, Lehrstuhl für Angewandte Mathematik und Numerische Analysis, Wuppertal, Germany;3. Laboratoire Paul Painlevé, CNRS UMR 8524, Villeneuve d'Ascq Cedex, France |
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| Abstract: | We consider the derivation of continuous and fully discrete artificial boundary conditions for the linearized Korteweg–de Vries equation. We show that we can obtain them for any constant velocities and any dispersion. The discrete artificial boundary conditions are provided for two different numerical schemes. In both continuous and discrete case, the boundary conditions are nonlocal with respect to time variable. We propose fast evaluations of discrete convolutions. We present various numerical tests which show the effectiveness of the artificial boundary conditions.© 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1455–1484, 2016 |
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| Keywords: | artificial boundary conditions KdV equation numerical simulation |
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