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arXiv · 1712.07547

Discrete energy estimates for the abcd-systems

Cosmin Burtea·Clémentine Courtès
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Abstract

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 $O(Δt+(Δx)^2)$ accurate, while if $bd=0$, we obtain an $O(Δt+Δx)$ -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.

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Cosmin Burtea, Clémentine Courtès. 2018-10-29. Discrete energy estimates for the abcd-systems. https://arxiv.org/abs/1712.07547

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