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Journal Articles Communications in Mathematical Sciences Year : 2019

Discrete energy estimates for the abcd-systems

Cosmin Burtea
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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(∆t + (∆x)^2) accurate, while if bd = 0, we obtain an O(∆t + ∆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.
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Dates and versions

hal-01669267 , version 1 (20-12-2017)
hal-01669267 , version 2 (29-10-2018)



Cosmin Burtea, Clémentine Courtès. Discrete energy estimates for the abcd-systems. Communications in Mathematical Sciences, 2019, 17 (1), pp.243-298. ⟨10.4310/CMS.2019.v17.n1.a10⟩. ⟨hal-01669267v2⟩
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