High-Accuracy Numerical Approximations to Several Singularly Perturbed Problems and Singular Integral Equations by Enriched Spectral Galerkin Methods
Year: 2020
Author: Sheng Chen
Journal of Mathematical Study, Vol. 53 (2020), Iss. 2 : pp. 143–158
Abstract
Usual spectral methods are not effective for singularly perturbed problems and singular integral equations due to the boundary layer functions or weakly singular solutions. To overcome this difficulty, the enriched spectral-Galerkin methods (ESG) are applied to deal with a class of singularly perturbed problems and singular integral equations for which the form of leading singular solutions can be determined. In particular, for easily understanding the technique of ESG, the detail of the process are provided in solving singularly perturbed problems. Ample numerical examples verify the efficiency and accuracy of the enriched spectral Galerkin methods.
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/jms.v53n2.20.02
Journal of Mathematical Study, Vol. 53 (2020), Iss. 2 : pp. 143–158
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Singularly perturbed problems weakly singular integral equations boundary layers enriched spectral Galerkin methods Jacobi polynomials.
Author Details
-
An exponential convergence approximation to singularly perturbed problems by Log orthogonal functions
Chen, Sheng | Zhang, ZhiminCalcolo, Vol. 59 (2022), Iss. 3
https://doi.org/10.1007/s10092-022-00470-9 [Citations: 1] -
Efficient function approximation in enriched approximation spaces
Herremans, Astrid | Huybrechs, DaanIMA Journal of Numerical Analysis, Vol. (2024), Iss.
https://doi.org/10.1093/imanum/drae017 [Citations: 0] -
Log orthogonal functions: approximation properties and applications
Chen, Sheng | Shen, JieIMA Journal of Numerical Analysis, Vol. 42 (2022), Iss. 1 P.712
https://doi.org/10.1093/imanum/draa087 [Citations: 15]