两组色散方程三层高精度显格式

Two groups of three-level high-precision explicit schemes for dispersive equation

针对色散方程u/t=a3u/x3,a为常数的初边值问题,采用组合差商法,构造了两组互为对称带参数的三层四点显式差分格式.格式的局部截断误差阶为O(τ2+h4),稳定性条件为0<|r|≤1/4.当其中的参数满足一定的条件后,格式的精确度可以提高到O(τ2+h6),稳定性条件为0<|r|≤1/60.这是两组高精度差分格式.最后用数值例子验证了理论分析的正确性.

For solving the initial boundary value problem of the dispersive equation ut=auxxx,two groups of symmetrical explicit schemes were designed by combining difference solution.They were containing parameters and three-level with four net points in the middle level.Their truncation errors were O（τ^2＋h^4）and stability conditions were 0｜r｜≤1/4.When the parameters satisfied some relation,the precise of the schemes could be improved to O（τ^2＋h^6）.At this time,the stability conditions were 0〈｜r｜≤1/60.The precise of these schemes were high.The last numerical example proves the theoretical analysis is correct.