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Volume 11, Issue 4
Asymptotic Analysis and a Uniformly Convergent Numerical Method for Singular Perturbation Problems

Anning Liu & Zhongyi Huang

DOI: 10.4208/eajam.291220.120421

East Asian J. Appl. Math., 11 (2021), pp. 755-787.

Published online: 2021-08

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  • 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.

  • Keywords

Tailored finite point method, singular perturbation problem, asymptotic analysis

  • AMS Subject Headings

65N35, 35C20

  • Copyright

COPYRIGHT: © Global Science Press

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@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} }
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.

Liu , Anning and Huang , Zhongyi. (2021). Asymptotic Analysis and a Uniformly Convergent Numerical Method for Singular Perturbation Problems. East Asian Journal on Applied Mathematics. 11 (4). 755-787. doi:10.4208/eajam.291220.120421
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