一种非等距网格差分格式求解含双边界层的反应扩散问题  

A non-equidistant grid difference scheme for solving reaction-diffusion problem with dual layers

作　　者：杜金月 王彩华[1] 张文逸 DU Jinyue;WANG Caihua;ZHANG Wenyi(College of Mathematical Science, Tianjin Normal University, Tianjin 300387, China)

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）》2018年第6期1-5,共5页Journal of Tianjin Normal University：Natural Science Edition

基　　金：天津市高等学校创新团队培养计划资助项目(TD13-5078)

摘　　要：研究二阶含双边界层的反应扩散问题.首先,在较粗的等距节点上采用含拟合因子的差分格式,并利用原微分方程关于小参数的渐近展开式来确定该因子,得到一组预估解;然后,将区间剖分为3个区域:左边界层区域、解平稳的中间区域和右边界层区域,在2个边界层区域加密剖分,采用含有拟合因子的差分格式再次计算,区域边界条件由预估解给出,中间区域利用二阶中心差分格式计算.数值实验表明本文方法计算效果较好,优于全区间上的中心差分格式以及含拟合因子的差分格式,有利于观察双边界层附近的数值解.The second order reaction-diffusion problem with dual layers is studied.Firstly,the difference scheme containing the fitting factor is adopted on the coarser equidistant nodes,and the factor is determined by the asymptotic expansion of the solution of the original differential equation,and then a set of predictor solutions is obtained.Then the interval is divided into three regions:the left boundary layer region,the smooth intermediate region and the right boundary layer region.The nodes in the boundary layer area are further refined,the boundary conditions are given by the prediction solution,and the difference scheme with fitting factor is calculated again.The second order central difference scheme is used in the smooth intermediate region.The numerical results show that this method is better than the central difference scheme and the difference scheme with fitting factor in the whole region,especially more advantageous to observe the numerical solution near the dual layers.

关 键 词：非等距网格 差分格式 双边界层 拟合因子 数值解 

分 类 号：O241.8[理学—计算数学]