一类奇异摄动边值问题的一致收敛迎风差分方法  

Uniformly Convergent Upwind Difference Approximation for a Singularly Perturbed Boundary Value Problem

作　　者：杨继明 YANG JIMING(School of Computational Science and Electronics,Hunan Institute of Engincering,Xiangtan 411104,China)

机构地区：[1]湖南工程学院计算科学与电子学院,湘潭411104

出　　处：《应用数学学报》2021年第2期269-278,共10页Acta Mathematicae Applicatae Sinica

基　　金：湖南省自然科学基金(2020JJ4242,2019JJ50105)资助项目。

摘　　要：对于一类奇异摄动边值问题,基于等分布弧长控制函数构建网格,提出了一种迎风差分方法.利用先验截断误差估计,基于离散比较原理和障碍函数技巧,证明了该方法得到的逼近解在最大模下是不依赖于摄动参数且一阶一致收敛的.收敛性分析是在整个区域上进行的,不需要对区域进行子区域的划分.为了验证理论分析,给出了数值实验结果.An upwind difference approximation is proposed on a mesh constructed by equidistributing the arc-length monitor function for a singularly perturbed boundary value problem.Uniformly first-order convergent solutions in the maximum norm are obtained independent of the perturbation parameter based on the priori truncation error estimates,the discrete comparison principle and the barrier function technique.The convergence analysis is carried out in the whole domain instead of dividing the domain into subregions.Numerical results are presented to verify the theoretical analysis.

关 键 词：奇异摄动问题 迎风差分 一致收敛 

分 类 号：O241.81[理学—计算数学]