求解奇异摄动两点边值问题的奇性分离法  

The Singularity-Separated Method for the Singularly Perturbed Two-Point Boundary Value Problem

作　　者：杨婧[1] 

机构地区：[1]湖南农业大学信息与智能科学技术学院,湖南 长沙

出　　处：《理论数学》2021年第12期2111-2115,共5页Pure Mathematics

摘　　要：本文使用奇性分离法求解奇异摄动两点边值问题。首先通过修改边界条件得到弱奇性的第三边值辅助问题,将其解记为w(x),其次利用特征值构造一个奇异函数v(x),最后将原两点边值问题的解u(x)表示为u(x)=w(x)-v(x)。由于将解的奇性进行了分离,数值求解时不必使用局部加密网格。数值实验中边界层仅用1个单元的稀疏网格就能得到高精度的有限元解。The singularity-separated method is used to solve the singularly perturbed two-point boundary value problem. The third boundary value problem whose solution is w(x) is constructed by modifying the boundary-value condition and a singular function v(x) is constructed by the eigenvalues. Then the solution u(x) of the two-point boundary value problem can be expressed as w(x)-v(x). Numerical results show that the FE-solutions have the high accuracy instead of local refinement meshgrid.

关 键 词：奇异摄动 两点边值问题 奇性分离法 第三边值辅助问题 奇异函数 

分 类 号：O17[理学—数学]