色散方程两层绝对稳定隐格式  

Two Level and Absolutely Stable Implicit Schemes for Dispersive Equation

作　　者：花小琴[1] 张大凯[2] 胥德平[3] 

机构地区：[1]江苏科技大学数理学院,江苏镇江212003 [2]贵州大学理学院,贵州贵阳550025 [3]成都理工大学信息管理学院,成都610059

出　　处：《大学数学》2011年第6期96-99,共4页College Mathematics

摘　　要：对色散方程ut=auxxx的初边值问题,构造了两组带参数绝对稳定两层四点去心隐式差分格式,其截断误差为O(τ+h2).若适当选取参数,格式的精确度可高达O(τ+h3).若特殊的令某个节点前的系数为0,则得到二阶的半显格式.最后的数例验证了理论分析的正确性.这是两组灵活、实用的差分格式.In this paper, two groups partial-node implicit schemes have been designed for solving the initial boundary value problem of the dispersive equation ut=auxxx au They are two level and containing parameters. Their truncation error is O （τ＋h2） and absolutely stable. The precision can be improved to O （τ-h^3） with some suitable parameters. Let some coefficients of nodes be 0 , we can deduce two order semi-explicit difference schemes. At the end, the numerical example proves the result of theoretical analysis. The schemes are flexible and especially practicable.

关 键 词：色散方程 组合差商法 隐格式 半显格式 收敛性 

分 类 号：O241.82[理学—计算数学]