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Article Dans Une Revue Mathematical Methods in the Applied Sciences Année : 2018

Numerical analysis of a water wave model with a nonlocal viscous dispersive term using the diffusive approach

Résumé

In this paper, we numerically study the water wave model with a nonlocal viscous term $$u_t+u_x+\beta u_{xxx}+\sqrt{\nu}D^{1/2}u+\gamma u u_x=\alpha u_{xx}$$ where $$ D^{1/2}u(t)=\frac{1}{\sqrt{\pi}}\frac{\partial}{\partial t}\int_0^t \frac{u(s)}{\sqrt{t-s}}\mathrm{d}s $$ is the Riemann-Liouville half-order derivative in time. We propose and compare different numerical schemes based on the diffusive realizations of fractional operators.
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hal-01818120 , version 1 (17-03-2023)

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Paternité - Pas d'utilisation commerciale

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Serge Dumont, Imen Manoubi. Numerical analysis of a water wave model with a nonlocal viscous dispersive term using the diffusive approach. Mathematical Methods in the Applied Sciences, 2018, 41 (12), pp.4810-4826. ⟨10.1002/mma.4932⟩. ⟨hal-01818120⟩
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