一类奇异摄动问题有限差分逼近改进的一致收敛性  

Improved uniform convergence of a finite difference approximation to a kind of singularly perturbed problems

作　　者：杨继明[1] 

机构地区：[1]湖南工程学院理学院,湖南湘潭411104

出　　处：《浙江大学学报（理学版）》2013年第2期136-139,共4页Journal of Zhejiang University（Science Edition）

基　　金：湖南省教育厅优秀青年项目(11B032);湖南省科技计划项目(2011FJ4146);湖南省高校科技创新团队支持计划资助项目

摘　　要：对于一类奇异摄动问题,给出了一种半离散差分格式,其网格是通过等分布所研究问题解的弧长控制函数而生成的.通过采用离散最大模原理和先验截断误差估计,证明了离散最大模下数值解是关于摄动参数ε一阶一致收敛的.这比已有文献中的误差收敛阶有明显的改进.数值实验验证了理论分析的正确性.For a kind of singularly perturbed problems, a semi-discretised approximation is investigated, in which the mesh is constructed adaptively by equidistributing the standard are-length monitor function of the solution. Based on the discrete maximum principle and a priori truncation error estimate, the error of the numerical solution in the dis- crete maximum norm is achieved, first-order uniformly convergent with respect to the perturbation parameter ∈. Comparing with the existing literature, the error convergence order in the current work has been greatly improved. The experiment is carried out, which coincides with the theorectical analysis.

关 键 词：一致收敛 奇异摄动 等分布 

分 类 号：O241.82[理学—计算数学]