含两个小参数的抛物对流扩散方程的有限差分法  

ANALYSIS OF A FINITE DIFFERENCE SCHEME FOR A PARABOLIC CONVECTION-DIFFUSION PROBLEM WITH TWO SMALL PARAMETERS

作　　者：岑仲迪[1] 

机构地区：[1]浙江万里学院数学研究所,宁波315100

出　　处：《系统科学与数学》2009年第7期888-901,共14页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(10671180);浙江省自然科学基金(Y607504);宁波市自然科学基金资助课题

摘　　要：研究含有两个小参数的奇异摄动抛物对流扩散方程的有限差分法。应用极大模原理和障碍函数技巧,可得方程的准确解及其各阶导数的界的估计。基于准确解的有关性态,构造分片一致的Shishkin型网格。在Shishkin型网格上构建一个隐式迎风差分格式来进行数值求解,证得此差分策略是关于两个小参数都一致一阶收敛的。数值实验证实了理论结果的正确性。In this paper a parabolic convection-diffusion problem with two small parameters is considered. By using the maximum principle with carefully chosen barrier functions, we obtain the estimates of bounds for the exact solution and its derivatives. A fully implicit upwind finite difference scheme on a Shishkin-type mesh is used to solve the problem numerically. It is shown that the scheme converge almost first-order uniformly with respect to two small parameters. Numerical results support the theoretical results.

关 键 词：奇异摄动 对流扩散 有限差分法 SHISHKIN网格 一致收敛 

分 类 号：O241.82[理学—计算数学] TN011[理学—数学]