TY - JOUR
T1 - A Family of Difference Schemes with Four Near-Conserved Quantities for the KdV Equation
AU - Han , Zhen
AU - Shen , Longjun
JO - Journal of Computational Mathematics
VL - 2
SP - 129
EP - 140
PY - 1998
DA - 1998/04
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9147.html
KW - Convergence, difference scheme, KdV equation, conserved quantity.
AB - <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>