Convergence of finite difference schemes for the Benjamin-Ono equation
Analysis of PDEs
2016-04-27 v2 Numerical Analysis
Abstract
In this paper, we analyze finite difference schemes for Benjamin-Ono equation, u_t = uu_x + Hu_{xx}, where H denotes the Hilbert transform. Both the decaying case on the full line and the periodic case are considered. If the initial data are sufficiently regular, fully discrete finite difference schemes shown to converge to a classical solution. Finally, the convergence is illustrated by several examples.
Keywords
Cite
@article{arxiv.1408.3948,
title = {Convergence of finite difference schemes for the Benjamin-Ono equation},
author = {Rajib Dutta and Helge Holden and Ujjwal Koley and Nils Henrik Risebro},
journal= {arXiv preprint arXiv:1408.3948},
year = {2016}
}
Comments
22 pages, 2 figures