Asymptotic Analysis and a Uniformly Convergent Numerical Method for Singular Perturbation Problems

Asymptotic Analysis and a Uniformly Convergent Numerical Method for Singular Perturbation Problems

Year:    2021

Author:    Anning Liu, Zhongyi Huang

East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 4 : pp. 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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.291220.120421

East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 4 : pp. 755–787

Published online:    2021-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    33

Keywords:    Tailored finite point method singular perturbation problem asymptotic analysis

Author Details

Anning Liu

Zhongyi Huang