中文摘要：

利用有限差分法逼近变系数广义ZK（Zakharov-Kuznetsov）方程的初边值问题,建构一个三层线性化隐式差分格式.利用离散能量估计方法,讨论差分格式解的唯一性以及x方向的一阶差商在L∞模意义下的收敛性、稳定性和收敛阶数,并通过数值算例验证理论分析的结果.

英文摘要：

In this paper,by using finite difference method,an implicit difference scheme is constructed to approximate the initial-boundary value problem of ZK equation.The proposed scheme is a three-level linearization scheme.Using the method of discrete energy estimates,existence uniqueness of difference scheme is proved.With the method of the discrete energy estimate,it is shown that the difference scheme is convergent in maximum norm.The convergence order is second-order in both space and time.Some numerical experiments are conducted to illustrate the theoretical results of the proposed difference scheme.