非等距网格上奇异扰动问题的有限差分格式  

A finite difference scheme for solving singular perturbation problems on non-equidistant grids

作　　者：郑尚昆[1] 王彩华[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）》2014年第3期11-16,共6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：考虑一维定常对流扩散方程的Dirichlet边值问题,利用Taylor级数构造一个基于非等距网格的有限差分格式,给出了格式的截断误差估计,并分析了其稳定性.采用网格生成函数构造非等距网格,并与一些已有的差分格式对比,数值实验表明该格式可以得到更为精确的数值结果,能很好地模拟边界层效应.The finite difference scheme for one dimensional steady convection-diffusion equation with Dirichlet boundary value problem on non-equidistant grids is derived by using Taylor series expansion method, the truncation error estimate and stability analysis of the scheme are given. A non-equidistant grid is constructed by using grid generation function. Numerical experiments show that the scheme can obtain more accurate results comparing with some schemes in literature, and the boundary layer effect can be well simulated.

关 键 词：奇异扰动问题 非等距网格 有限差分格式 截断误差估计 

分 类 号：O241.82[理学—计算数学]