奇异摄动问题向前差商迎风格式移动网格收敛性分析  

Convergence Analysis for a Singularly Perturbed Problem Using the Forward Upwind Difference Scheme on Adaptive Meshes

作　　者：刘莺[1] 陈艳萍[2] 

机构地区：[1]湖南农业大学理学院,湖南长沙410128 [2]华南师范大学数学科学学院,广东广州510631

出　　处：《湘潭大学自然科学学报》2009年第2期8-11,共4页Natural Science Journal of Xiangtan University

基　　金：教育部"新世纪优秀人才支持计划"(NCET-04-0776);国家自然科学基金资助项目(10371104);国家973项目"高性能科学计算研究"子课题(2005CB321703)

摘　　要：带有指数边界层的奇异摄动两点边值问题能在自适应网格上有效解出.这种网格是通过等分布一个区域上的控制函数而产生.选用对方程两阶导数为向前差商的迎风差分格式,对控制函数M(x)取值为1+(ε-1e-βx/ε)2,利用离散的格林函数可得不依赖于摄动参数ε的收敛结果,误差阶和加权误差导数的阶均为O(N-1).A singularly perturbed two-point boundary value problem with an exponential boundary layer is solved numerically by using an adaptive grid method. The mesh is constructed adaptively by equidistributing a monitor function over the domain of the problem. In this paper, we choose the forward upwind difference scheme and set M（x） =√1＋（ε^-1e^βrε）^2. By using the discrete Green＇s function,a convergent result which is independent of the perturbation parameter is obtained. The order is O（N^-1 ）. And the error bound for the weighted derivative is established. The order is also O（ N^-1）.

关 键 词：奇异摄动问题 迎风差分格式 等分布原理 一致收敛性 

分 类 号：O241.82[理学—计算数学]