广义对称正则长波方程的新型守恒差分逼近  

A new conservative finite difference method for generalized symmetric regularized long wave equation

作　　者：郑茂波[1] 胡劲松[2] 胡兵[3] 

机构地区：[1]成都电子机械高等专科学校,成都610031 [2]西华大学数学与计算机学院,成都610039 [3]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2011年第6期1269-1275,共7页Journal of Sichuan University(Natural Science Edition)

摘　　要：作者对一类广义对称正则长波方程的初边值问题进行了数值研究,提出了一个带有加权系数θ的平均隐式差分格式,格式模拟了初值问题的守恒性质,得到了差分解的存在唯一性,并利用离散泛函分析方法分析了该格式的二阶收敛性与稳定性.数值结果表明,该格式是可信的,且适当地调整加权系数θ,可以使计算结果具有更高的精度.In this paper, a finite different method for an initial-boundary value problem of generalized symmetric regularized long wave equation is considered. An average implicit and energy conservative finite difference scheme with the weighted coefficient θ is proposed. Existense and uniqueness of the numerical solutions are shown. The second-order convergence and the stability of the numerical solutions are proved by the discrete functional analysis. Numerical experiments show that this method is efficient and making appropriate adjustments to the weighted coefficient θ would make calculations with higher precision.

关 键 词：广义对称正则长波方程 差分格式 守恒 收敛性 稳定性 

分 类 号：O241.82[理学—计算数学]