摘要
考虑带大Reynolds数问题的对流-扩散方程.近年来Shishkin网格法适合这类总是的求解,收敛阶为O(N-1lnN).提出高精度方法,首先解析解被分解为光滑部分和奇性部分,按Shishkin过渡点进行不等距网格剖分.光滑部分使用了Runge-Kutta方法;对于奇性部分,除了采用指数拟合方法外,还结合零逼近技巧,这样构造的混合方法是高精度的.最后本文给出数值例子以说明理论结果的正确性.
In this paper convection diffusion problem with big Reynolds number is considered. Shishkin＇s method has become popular for this kind of problem in recent years. It is uniformly convergent with respect to big Reynolds number in order O（N^-1 lnN）. In this paper,high accurate numerical method is presented by mixed method. Firstly,the analytic solution is decomposed into the smooth component and the singular component. Secondly,the non-equidistant mesh partition according to Shishkin＇s transition point is considered. Thirdly,Runge-Kutta method is applied for the smooth component. For the singular component, the exponentially fitted difference scheme with zero approximate techinique is used. The new method is shown that it is a high accurate method. Finally,numerical result is given,which is in agreement with the theoretical result.
出处
《厦门大学学报（自然科学版）》
CAS
CSCD
北大核心
2007年第1期18-20,共3页
Journal of Xiamen University：Natural Science
基金
福建省自然科学基金(2006J0040)
集美大学博士科研经费(ZQ2006034)资助
关键词
奇摄动
对流扩散
数值方法
singular perturbation
convection diffusion problem
numerical solution
