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Discrete artificial boundary conditions for the linearized Korteweg–de Vries equation
Author(s) -
Besse C.,
Ehrhardt M.,
LacroixViolet I.
Publication year - 2016
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22058
Subject(s) - korteweg–de vries equation , mathematics , boundary (topology) , boundary value problem , mathematical analysis , constant (computer programming) , partial differential equation , variable (mathematics) , physics , nonlinear system , computer science , quantum mechanics , programming language
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