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
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。
Abstract: 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.
文章引用：杨婧. 求解奇异摄动两点边值问题的奇性分离法[J]. 理论数学, 2021, 11(12): 2111-2115. https://doi.org/10.12677/PM.2021.1112236

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