一种非均匀网格上的高精度紧致差分格式  

A higher accurate compact difference scheme on non-uniform grid

作　　者：孙建安[1] 贾伟[1] 吴广智[1] 

机构地区：[1]西北师范大学物理与电子工程学院,甘肃兰州730070

出　　处：《西北师范大学学报（自然科学版）》2014年第4期31-35,40,共6页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(10875098);西北师范大学科技创新工程资助项目(NWNU-KJCXGC-0348)

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.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.

关 键 词：非均匀网格 紧致差分格式 数值解 BURGERS方程 对流方程 

分 类 号：O241.82[理学—计算数学]