求解广义BBM-Burgers方程的一个两层非线性守恒差分格式  

Two Level Nonlinear Conservative Difference Scheme for Solving Generalized BBM-Burgers Equation

作　　者：胡劲松[1] 王婷婷[1] 陈涛[1] 

机构地区：[1]西华大学理学院,四川成都610039

出　　处：《西华大学学报（自然科学版）》2015年第3期89-93,96,共6页Journal of Xihua University:Natural Science Edition

基　　金：四川省教育厅青年基金(11ZB009)

摘　　要：对广义BBM-Burgers方程的初边值问题进行了数值研究,提出一个两层非线性Crank-Nicolson差分格式,格式合理地模拟方程本身的一个守恒量,得到差分解的先验估计和存在唯一性,并利用能量方法分析该格式的二阶收敛性与无条件稳定性。In this paper, a two level nonlinear Crank-Nicolson difference scheme is proposed. The scheme provides a numerical solution to the initial boundary value problem of general BBM-Burgers equation. A conservative variable of the equation is simulated well with the scheme. In the simulation, the prior estimate and uniqueness of the solution are also obtained. In addition, the second or- der convergence and unconditional stability are proved by using energy analysis.

关 键 词：广义 BBM—Burgers方程 差分格式 守恒 收敛性 稳定性 

分 类 号：O241.8[理学—计算数学]