TY - JOUR
T1 - A Fourth-Order Compact and Conservative Difference Scheme for the Generalized Rosenau-Korteweg de Vries Equation in Two Dimensions
AU - Wang , Jue
AU - Zeng , Qingnan
JO - Journal of Computational Mathematics
VL - 4
SP - 541
EP - 555
PY - 2019
DA - 2019/06
SN - 37
DO - http://doi.org/10.4208/jcm.1810-m2016-0774
UR - https://global-sci.org/intro/article_detail/jcm/13211.html
KW - RKdV equation, Conservation, Existence, Uniqueness, Stability, Convergence.
AB - <p style="text-align: justify;">In this paper, a conservative difference scheme for the Rosenau-Korteweg de Vries
(RKdV) equation in 2D is proposed. The system satisfies the conservative laws in energy
and mass. Existence and uniqueness of its difference solution have been shown. The order
of $O(τ^2 +h^4)$ in the discrete $L^∞$-norm with time step $τ$ and mesh size $h$ is obtained. Some
important lemmas are proposed to prove the high order convergence. We prove that the
present scheme is unconditionally stable. Numerical results are also given in order to check
the properties of analytical solution.</p>