色散方程两层稳定的偏心隐格式

Two Groups Partial-node Implicit Schemes for Dispersive Equation

利用组合差商法对色散方程ut=auxxx的初边值问题,构造了两组带参数两层四点偏心隐式差分格式PL2,PR2,其截断误差为ο(τ+h2),稳定性随参数变化而变化。特殊的,若令某个节点前的系数为0,则得到二阶的半显格式。最后的数例既验证了理论分析的正确性,也说明了特取参数可以增强格式应用的灵活性。

Two groups of partial-node implicit schemes P2^L and P2^R, which are two-level and contain parameters, are designed for solving the initial boundary value problem of the dispersive equation ut = auxxx with combined difference solution. Their truncation errors are o（τ＋h^2）and their stabilities depend on the parameters. Especially, let some coefficients of the nodes be 0, two order semi-explicit difference schemes can be deduced. The last numerical example not only proves the result from the theoretical analysis, but also shows that the pa- rameters in schemes can improve their flexibility.