摘要
对流扩散方程可以描述众多的物理化学现象,因而对其寻求稳定的、实用的数值解法有着重要的现实意义.本文针对形式较一般的一维非定常对流扩散方程.构造了对角元严格占优的Crank-Nicholson差分格式.然后对其分别用分离变量的方法以及能量估计的方法作了稳定性的分析,最后给出了数值试验的结果,数值结果表明本文构造的格式能够较好的处理经典的Crank-Nicholson格式所不能处理的对流项系数较大的对流扩散方程.并具有较好的精度.
Convection-diffusion equation can describe a lot of physical and chemical phenomena, so to secure a stable and practical numerical solution method is very critical. This article establishes a new Crank-Nicholson difference scheme that produce a matrix which is diagonal-dominated. Stability is analyzed by using Fourier method and energy method. At last, a result of numerical experiment is given. The result shows that this scheme can well handle with the Convection-diffusion equation whose convection term has a bigger coefficient, while the classical scheme can not.
出处
《数学杂志》
CSCD
北大核心
2003年第1期37-42,共6页
Journal of Mathematics
基金
国家自然科学基金资助项目(19771062)
