Convergence of a higher-order scheme for Korteweg-de Vries equation
Analysis of PDEs
2014-08-18 v1
Abstract
We study the convergence of higher order schemes for the Cauchy problem associated to the KdV equation. More precisely, we design a Galerkin type implicit scheme which has higher order accuracy in space and first order accuracy in time. The convergence is established for initial data in L^2, and we show that the scheme converges strongly in L^2(0,T; L^2_loc(\R)) to a weak solution. Finally, the convergence is illustrated by several examples.
Keywords
Cite
@article{arxiv.1408.3552,
title = {Convergence of a higher-order scheme for Korteweg-de Vries equation},
author = {Rajib Dutta and Ujjwal Koley and Nils Henrik Risebro},
journal= {arXiv preprint arXiv:1408.3552},
year = {2014}
}
Comments
20 pages, 2 figures