对流扩散方程的高精度多步显式差分格式  

Highly Accurate Multistep Explicit Scheme for Convection-Diffusion Equation

作　　者：赵玲玲[1] 王霞[1] 

机构地区：[1]郑州轻工业学院信息与计算科学系,郑州450002

出　　处：《河南科学》2007年第3期348-350,共3页Henan Science

基　　金：国家自然科学基金项目(10371111);郑州轻工业学院校内基金项目(2004xjj013)

摘　　要：为提高对流扩散方程的显式差分格式的数值计算精度和效率,提出了一种新的高精度多步显式格式.空间坐标按高精度差分法离散,时间方向作数值积分,给出几种不同的差分格式.利用精确解给出初边值条件,利用Matlab软件编程求出数值解,并与加罚C-N格式的数值解做了比较,数值结果表明,该格式具有精度高且可以进行长时间稳定计算的优点.A highly accurate multistep explicit scheme for convection-diffusion equation is proposed in order to improve accuracy and efficiency of explicit difference scheme. The space derivatives are discretized with respect to high accurate difference method, and integration is used on time. A kind of finite-difference schemes are obtained. It＇s initial-boundary value conditions are valued by exact solution. We obtain numerical solution of convection-diffusion equation using Matlab software and compare the numerical solution with that of adjoining penalty function C-N scheme. The mumerical results show that the scheme of this artical has some advantages which are high precision and long computing time to compute stablely.

关 键 词：对流扩散方程 数值解 有限差分格式 高精度 

分 类 号：O241.81[理学—计算数学]