CAJ | 학술논문

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0（τ＋h^2）．若适当选取参数，格式的精确度可高达0（τ＋h^3）．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．
대색산방정ut=auxxx적초변치문제，구조료량조대삼수절대은정량층사점거심은식차분격식，기절단오차위0（τ＋h^2）．약괄당선취삼수，격식적정학도가고체0（τ＋h^3）．약특수적령모개절점전적계수위0，칙득도이계적반현격식．최후적수례험증료이론분석적정학성．저시량조령활、실용적차분격식．
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.