English

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