Numerical Investigation of the Decay Rate of Solutions to Models for Water Waves with Nonlocal Viscosity
Year: 2013
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 2 : pp. 333–349
Abstract
In this article, we investigate the decay rate of the solutions of two water wave models with a nonlocal viscous term written in the KdV form $$u_t+u_x+\beta u_{xxx}+\frac{\sqrt v}{\sqrt \pi}\int^t_0\frac{u_t(s)}{\sqrt{t-s}}ds+uu_x=vu_{xx}$$ and $$u_t+u_x-\beta u_{txx}+\frac{\sqrt v}{\sqrt \pi}\int^t_0\frac{u_t(s)}{\sqrt{t-s}}ds+uu_x=vu_{xx}$$ in the BBM form. In order to realize this numerical study, a numerical scheme based on the $G^{\alpha}$-scheme is developed.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-IJNAM-571
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 2 : pp. 333–349
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: waterwaves viscous asymptotical models long-time asymptotics fractional derivatives.