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中文摘要：
提出了一种形式简单、网格剖分灵活、具有一定通用性的非均匀网格上的三点四阶紧致差分格式,对格式的截断误差进行了分析.采用文中提出的格式对Burgers方程和对流方程进行数值求解,并与均匀网格上的三点四阶紧致差分格式所得数值解对比,结果证明本文提出的格式对于大梯度问题的数值模拟有更高的精度.
英文摘要：
A third-point fourth-order compact difference scheme is proposed on the non-uniform grid,which is simple in form,flexible in grid subdivision and general in use.The truncation error of the scheme is analyzed.The Burgers equation and the convection equation are solved numerically by using present scheme,the numerical solutions are compared with those obtained from the standard third-point fourth-order compact difference scheme on the uniform grid,and the results show that the present scheme have higher accuracy for large gradient problems.
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