Camassa-Holm方程的Crank-Nicolson守恒差分格式  

The Crank-Nicolson conservative finite difference scheme for Camassa-Holm equation

作　　者：常红[1] 丁丹平[2] CHANG Hong;DING Danping(School of Engineering and Architecture,Shaanxi Radio & TV University,Xi’an,Shaanxi 710119,China;School of Science,Jiangsu University,Zhenjiang,Jiangsu 212013,China)

机构地区：[1]陕西广播电视大学工程与建筑学院,陕西西安710119 [2]江苏大学理学院,江苏镇江212013

出　　处：《贵州师范大学学报（自然科学版）》2019年第5期85-90,共6页Journal of Guizhou Normal University：Natural Sciences

基　　金：国家自然科学基金项目(11371175);陕西广播电视大学校级课题(15D-07-B02)

摘　　要：针对Camassa-Holm方程的初边值问题建立了一种非线性的两层Crank-Nicolson守恒差分格式,验证了该差分格式解的存在性以及能量守恒性,对差分解进行了模估计,并用离散能量方法证明了该差分格式解的收敛性和稳定性,最后用数值实验验证了差分解的精确性。A two-level nonlinear Crank-Nicolson conservative finite difference scheme is estabilished for Camassa-Holm equation with dirichlet boundary value condition in this paper,the existence of the difference solution and the energy conservation of the solution of the difference equation is proved,the solution of the scheme is estimated,the unconditionally stability and convergence of the difference scheme is proved.

关 键 词：CAMASSA-HOLM方程 CRANK-NICOLSON差分格式 收敛性 稳定性 

分 类 号：O241[理学—计算数学]