Neumann边界条件的处理对差分解逼近精度的影响

计算物理 ›› 1992, Vol. 9 ›› Issue (4): 461-463.

Neumann边界条件的处理对差分解逼近精度的影响

黄维章, 张锁春

中国科学院应用数学研究所, 北京 100080

收稿日期:1992-03-06 出版日期:1992-12-25 发布日期:1992-12-25

THE EFFECT OF TREATMENT OF NEUMANN BOUNDARY CONEITI ONS ON THE ACCURACY OF FINITE DIFFERENCE SOLUTIONS

Huang Wei-zhang, Zhang Suo-Chun

Institute of Applied Mathematics, Academia Sinica P. O. Box 2734, Beijing 100080, China

Received:1992-03-06 Online:1992-12-25 Published:1992-12-25

摘要/Abstract

摘要： 本文以一维对流扩散方程为例,较系统地论证了Neumann边界的差分处理对差分解逼近精度的影响。并从数值上考察了Neumann边界的差分处理对二维Poisson方程差分解的影响。结果表明:O(h)格式可能导致一阶精度的差分解,也可能导致二阶精度的差分解;而O(h²)和O(h³)格式产生的差分解只有二阶精度。

关键词: Neumann边界, 差分解, 逼近精度

Abstract: In this paper, we are devoted to a study of the effect of the treatment of Neumann boundary conditions for one-dimensional advection-diffusion equation by the analysis method, and for tow-dimensional Poisson equation by the numerical test method. The reults show that the scheme is first-order accurate in space (i.e. O(h)can be derived first-order accurate difference solution or second-order solution, and the O(h²) or O(h³) scheme is only derived second-order solution.

Key words: Neumann Boundary, Difference Solution, Accuracy

黄维章, 张锁春. Neumann边界条件的处理对差分解逼近精度的影响[J]. 计算物理, 1992, 9(4): 461-463.

Huang Wei-zhang, Zhang Suo-Chun. THE EFFECT OF TREATMENT OF NEUMANN BOUNDARY CONEITI ONS ON THE ACCURACY OF FINITE DIFFERENCE SOLUTIONS[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1992, 9(4): 461-463.