@Article{EAJAM-11-755, author = {Liu , Anning and Huang , Zhongyi}, title = {Asymptotic Analysis and a Uniformly Convergent Numerical Method for Singular Perturbation Problems}, journal = {East Asian Journal on Applied Mathematics}, year = {2021}, volume = {11}, number = {4}, pages = {755--787}, abstract = {

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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.291220.120421 }, url = {http://global-sci.org/intro/article_detail/eajam/19371.html} }