中文摘要：

针对Burgers方程,采用余项修正法和欧拉公式,推导了一种新的四层高精度紧致差分隐格式,其截断误差为O（τ^2＋τh^2＋h^4）,即当τ=O（h^2）时,格式空间具有四阶精度;然后通过数值实验验证了格式的精确性和可靠性.

英文摘要：

A four-level high order compact finite difference implicit scheme is proposed for solving the Burgers equation.The error remainder correction method and the Euler formula are adopted.The local truncation error of the scheme is O（τ^2 ＋ τh^2 ＋ h^4）,i.e.,the scheme is the fourth order accuracy for space when τ= O（h^2）.Then,numerical experiments are conducted to verify the accuracy and the reliability of the present scheme.