耗散对称正则长波方程的有限差分逼近  

FINITE DIFFERENCE APPROXIMATE SOLUTION FOR DISSIPATIVE SYMMETRIC REGULARIZED LONG WAVE EQUATION

作　　者：胡劲松[1] 胡兵[2] 徐友才[2] 

机构地区：[1]西华大学数学与计算机学院,成都610039 [2]四川大学数学学院,成都610064

出　　处：《计算数学》2011年第2期177-184,共8页Mathematica Numerica Sinica

摘　　要：本文对耗散对称正则长波方程的初边值问题进行了数值研究,提出了一个两层隐式Crank-Nicolson差分格式,讨论了差分解的存在唯一性,并利用能量方法分析了该格式的二阶收敛性与稳定性,数值算例表明本文的格式是可靠的.An implicit Crank-Nicolson scheme is proposed for the initial value problems of dissipative symmetric regularized long wave equation.The existence and uniqueness of the finite difference solution are proved.Additionally,a convergence of second order and unconditional stability are demonstrated by using the energy method.A numerical example is provided to illustrate the features of this method and confirm the theoretical results.

关 键 词：耗散对称正则长波方程 C-N差分格式 收敛性 稳定性 

分 类 号：O241.82[理学—计算数学]