非等距网格下二阶导数三阶精度差分格式的准确性分析  

Accuracy Analysis of the Sachem of Third-order Finite Difference of the Second Derivative on Non-uniform Grid

作　　者：李丽丽[1] 张昆[1] 王良璧[2] 常迎香[1] 

机构地区：[1]兰州交通大学数理与软件工程学院,甘肃兰州730070 [2]兰州交通大学机电工程学院,甘肃兰州730070

出　　处：《兰州交通大学学报》2008年第3期148-150,共3页Journal of Lanzhou Jiaotong University

摘　　要：利用Taylor展式系数匹配的方法得到基于非等距网格的二阶导数三阶精度的差分格式,并且对其进行了实例考察,得出此差分格式满足其精度要求,差分格式是合理可靠的.通过Fourier分析方法对其误差传播情况进行了分析,在不同网格比下,其逼近程度(精度)有所不同.当网格的比率大于1时,格式通常是稳定的,但对于高波分量的模拟效果较差;网格比率小于1时,虽然对高波分量的模拟效果较好,但格式是不稳定的.A third-order finite difference scheme is presented for the second derivative on non-uniform grid. The accuracy is good using the difference scheme in the example investigated here. The results show that this difference scheme is reasonable. To investigate the accuracy of the scheme on non-uniform grid system, Fourier analysis is performed. The Fourier analysis shows that the grid ratio plays a crucial role in the accu- racy of such scheme. The accuracy is different for different grid ratio. When the grid ratio is bigger than 1, the scheme is stable,but the result of simulation for high wave number is not good;when the grid ratio is smaller than 1, the out coming of simulation for high wave number is well, but the scheme is instable.

关 键 词：非等距网格 二阶导数 差分格式 FOURIER分析 

分 类 号：O241.4[理学—计算数学]