二维奇异扰动问题的非等距有限差分格式  

Finite difference scheme on non-uniform mesh for two-dimensional singularly perturbed problems

作　　者：李恬[1] 王彩华[1] 郑尚昆[1] 

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《天津师范大学学报（自然科学版）》2016年第3期8-12,共5页Journal of Tianjin Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11071123)

摘　　要：通过对一维非等距中心差分格式引入拟合因子,构造了一类新型非等距中心差分格式,将其推广到二维情形,得到一类针对二维奇异扰动问题的新型非等距五点差分格式,对该格式进行了截断误差估计.数值实验部分采用4种非等距网格进行处理,结果表明该非等距差分格式对含边界层的奇异扰动问题有很好的实用性.A new five-point finite difference scheme on non-uniform mesh by adding fitting factors to the central difference scheme is presented for two-dimensional singularly perturbed problems, and the truncation error estimate is given. Numeri- cal experiments are implemented on four kinds of non-uniform mesh, and the results show that the scheme is well applica- ble to singularly perturbed problems with boundary layers.

关 键 词：奇异扰动问题 非等距网格 有限差分格式 拟合因子 截断误差估计 

分 类 号：O241.82[理学—计算数学]