色散方程的十点隐式差分格式

色散方程的初边值问题是在孤立波这样的物理现象中抽象出来的一类数学模型,在前人构造的众多差分格式的基础上, 使用新的构造方法,给出了该问题的三层十点隐式差分格式.同时,应用多维泰勒公式计算出它的截断误差,并在此基础上利用离散傅立叶方法分析了稳定性,得出此格式恒稳定的结论.所构造的差分格式会为构造更复杂偏微分方程的差分格式提供有重要意义的价值参考.

Ten-point implicit difference schemes of the dispersive equation

The initial-boundary value problem of dispersive equation is a kind of mathematical model,in this paper,it has been followed the ways of other scholars and used a new method and got a new difference scheme.It was a three layers ten-point implicit difference schemes.At the same time,it has been calculated its truncation errors by using multi-dimensional Taylor formula and analyzed the stability by the discrete Fourier transform.At last,the conclusion of the stable difference schemes has been drawn.It can off...