@Article{JCM-16-2,
author = {Zhen, Han and Shen, Longjun},
title = {A Family of Difference Schemes with Four Near-Conserved Quantities for the KdV Equation},
journal = {Journal of Computational Mathematics},
year = {1998},
volume = {16},
number = {2},
pages = {129--140},
abstract = {<p style="text-align: justify;">We construct and analyze a family of semi-discretized difference schemes with two parameters for the Korteweg-de Vries (KdV) equation. The scheme possesses the first four near-conserved quantities for periodic boundary conditions. The existence and the convergence of its global solution in Sobolev space $\boldsymbol{L}_{\infty} (0, T;&nbsp;\boldsymbol{H}^3)$ are proved and the scheme is also stable about initial values. Furthermore, the scheme conserves exactly the first two conserved quantities in the special case.&nbsp;</p>},
issn = {1991-7139},
doi = {https://doi.org/1998-JCM-9147},
url = {https://global-sci.com/article/85677/a-family-of-difference-schemes-with-four-near-conserved-quantities-for-the-kdv-equation}
}