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 -

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.