@Article{IJNAM-15-102,
author = {Chen , Chuanmiao and Yang , Jing},
title = {The Singularity-Separated Method for the Singular Perturbation Problems in 1-D},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2018},
volume = {15},
number = {1-2},
pages = {102--110},
abstract = {<p style="text-align: justify;">The singularity-separated method (SSM) for the singular perturbation problem $-\epsilon u&#39;&#39;+bu&#39; + cu = f(x), u(0) = u(1) = 0$, is proposed for the first time. The solution is expressed as $u = w-ν$, where $w$ is the solution of corresponding third boundary value problem and $ν$ is an exact singular function. We have proved a global regularity, $||w||_2 ≤ C$, where the constant $C$ is independent of $\epsilon$, and discussed three kinds of finite element (FE) methods with SSM. Numerical results show that these FE-solutions have the high accuracy when only one element in boundary layer is taken.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/10558.html}
}