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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