Discrete energy estimates for the abcd-systems

Discrete energy estimates for the abcd-systems

In this article, we propose finite volume schemes for the $abcd$-systems and we establish stability and error estimates. The order of accuracy depends on the so-called BBM-type dispersion coefficients $b$ and $d$. If $bd>0$, the numerical schemes are $O(\Delta t+(\Delta x)^2)$ accurate, while if...

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Bibliographic Details
Main Authors: Burtea, Cosmin, Courtès, Clémentine
Format: Journal Article
Language:English
Published: 20-12-2017
Subjects:
Mathematics - Numerical Analysis
Online Access:Get full text
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Summary:In this article, we propose finite volume schemes for the $abcd$-systems and we establish stability and error estimates. The order of accuracy depends on the so-called BBM-type dispersion coefficients $b$ and $d$. If $bd>0$, the numerical schemes are $O(\Delta t+(\Delta x)^2)$ accurate, while if $bd=0$, we obtain an $O(\Delta t+\Delta x)$ -order of convergence. The analysis covers a broad range of the parameters $a,b,c,d$. In the second part of the paper, numerical experiments validating the theoretical results as well as head-on collision of traveling waves are investigated.
DOI:10.48550/arxiv.1712.07547