变系数Zakharov-Kuznetsov方程的三层线性隐式差分格式  

A three-level difference scheme for Zakharov-Kuznetsov equation

作　　者：盛秀兰[1,2] 冯美娇[1] 吴宏伟[1] 

机构地区：[1]东南大学数学系,南京210096 [2]江苏开放大学,南京210036

出　　处：《扬州大学学报（自然科学版）》2015年第2期31-34,39,共5页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11271068);江苏开放大学"十二五"规划课题(13SEW-C-076)

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.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.

关 键 词：ZAKHAROV-KUZNETSOV方程 隐式差分格式 收敛性 稳定性 

分 类 号：O241.82[理学—计算数学]