耗散SRLW方程的一个三层加权线性差分格式  

A Three Weighted Linear Differential Format Of Dissipative Symmetric Regularized Long Wave Equation

作　　者：林雪梅[1] 胡劲松[1] 刘倩[1] 

机构地区：[1]西华大学数学与计算机学院,四川成都610039

出　　处：《西华大学学报（自然科学版）》2014年第2期35-40,43,共7页Journal of Xihua University:Natural Science Edition

基　　金：四川省教育厅青年基金项目(11ZB009);西华大学研究生创新基金(ycjj201311)

摘　　要：对耗散对称正则长波方程的初边值问题进行了有限差分方法研究,提出了一个三层平均隐式加权差分格式,模拟了问题本身的2个守恒量,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。数值实验表明,本文提出的差分格式方法是可信的,且计算精度对加权系数具有一定的依赖性。In this paper ,a finite difference method is proposed for the initial value problems of dissipative symmetric regularized long wave equation was presented .An energy conservative implicit weighted finite difference of three levels was proposed .The scheme has the advantages that it preserves some invariant properties of the original differential equation .Existence and uniqueness of numerical solutions were derived,It is proved that the finite difference scheme is convergent in order O（τ2 ＋h2） and stable.The results attained form numerical experiments show that the feature of this method is reliable and efficient .

关 键 词：耗散对称正则长波方程 差分格式 守恒 收敛性 稳定性 

分 类 号：O241.82[理学—计算数学]