TY - JOUR
T1 - Asymptotic Analysis and a Uniformly Convergent Numerical Method for Singular Perturbation Problems
AU - Liu , Anning
AU - Huang , Zhongyi
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 755
EP - 787
PY - 2021
DA - 2021/08
SN - 11
DO - http://doi.org/10.4208/eajam.291220.120421 
UR - https://global-sci.org/intro/article_detail/eajam/19371.html
KW - Tailored finite point method, singular perturbation problem, asymptotic analysis
AB - <p style="text-align: justify;">Approximation methods for boundary problems for a fourth-order singularly
perturbed partial differential equation (PDE) are studied. Using a suitable variable
change, we reduce the problem to a second-order PDE system with coupled boundary
conditions. Taking into account asymptotic expansions of the solutions, we discrete the
resulting problem by a tailored finite point method. It is proved that the scheme converges uniformly with respect to the small parameter involved. Numerical results are
consistent with the theoretical findings.</p>