色散方程两组三阶恒稳显格式

Two Groups of Three Order Absolutely Stable Explicit Schemes for Dispersive Equation

采用组合差商法对色散方程ut=auxxx(a为常数)的初边值问题,构造了两组互为对称带参数的三层显式差分格式.它们空间宽度为4,其局部截断误差为O(τ+h3),绝对稳定.而且计算时无方向性的约束,即不管a的符号如何,每一组格式均可以计算.最后给出了数值例子,数值结果表明了理论分析的正确性.

Two groups of explicit schemes have been designed for solving the initial boundary value problem of the dispersive equation u, = auxxx by the combined difference quotient method. They are 3-level with weighting coefficients and symmetric in form. The schemes combined the net points in three time levels and four spacial columns. Their truncation errors are O（τ ＋ h^3） and absolutely stable. Above all, they will not be controlled by direction. The last numerical example proves the result of theoretical analysis.