@Article{JCM-16-129, author = {Han , Zhen 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 = {

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 $\boldsymbol{L}_{\infty} (0, T; \boldsymbol{H}^3)$ 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. 

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9147.html} }