Artificial boundary conditions for the linearized Benjamin-Bona-Mahony equation
type: Item
instance of: scholarly article
title: Artificial boundary conditions for the linearized Benjamin-Bona-Mahony equation
zbMATH Open document ID: 1397.65130
author: Christophe Besse
author: Benoît Mésognon-Gireau
author: Pascal Noble
published in: Numerische Mathematik
publication date: 2018-06-25T00:00:00Z
review text: The problem of modelling unidirectional propagation of weakly nonlinear, long waves in the presence of dispersion, among other things, is governed by the Benjamin-Bona-Mahony (BBM) equation. Normally, it is considered as an alternative to the Korteweg-de Vries equation, due to some of its analytical advantages. The authors study the linearized BBM equation. First, the continuous transparent boundary conditions are presented for the linearized BBM equation. Two accurate space and time discretizations of this equation are proposed and the process of deriving the discrete transparent boundary conditions is given. The consistency of the discrete transparent boundary conditions with the continuous ones is proved. The convergence of the numerical scheme relying on a stability analysis is also shown. Three types of numerical simulation are performed to illustrate the findings of the work.
reviewed by: Kanakadurga Sivakumar
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M85
Mathematics Subject Classification ID: 76M20
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 6894071
zbMATH Keywords: linear BBM equation
zbMATH Keywords: Benjamin-Bona-Mahony equation
zbMATH Keywords: upwind discretization
zbMATH Keywords: centered discretization
zbMATH Keywords: stability
zbMATH Keywords: convergence
zbMATH Keywords: consistency
zbMATH Keywords: discrete transparent boundary conditions
MaRDI profile type: Publication
full work available at URL: s00211-017-0943-1
OpenAlex ID: W2594208438
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DOI: 10.1007/S00211-017-0943-1
description: scientific article; zbMATH DE number 6894071